Abstract: Communications in Contemporary Mathematics, Ahead of Print. We give a complete characterization of the existence of Lyapunov coordinate changes bringing an invertible sequence of matrices to one in block form. In other words, we give a criterion for the block-trivialization of a nonautonomous dynamics with discrete time while preserving the asymptotic properties of the dynamics. We provide two nontrivial applications of this criterion: we show that any Lyapunov regular sequence of invertible matrices can be transformed by a Lyapunov coordinate change into a constant diagonal sequence; and we show that the family of all coordinate changes preserving simultaneously the Lyapunov exponents of all sequences of invertible matrices (with finite exponent) coincides with the family of Lyapunov coordinate changes. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:57Z DOI: 10.1142/S0219199717500274

Abstract: Communications in Contemporary Mathematics, Ahead of Print. We investigate the optimality problem associated with the best constants in a class of Bohnenblust–Hille-type inequalities for [math]-linear forms. While germinal estimates indicated an exponential growth, in this work we provide strong evidences to the conjecture that the sharp constants in the classical Bohnenblust–Hille inequality are universally bounded, irrespectively of the value of [math]; hereafter referred as the Universality Conjecture. In our approach, we introduce the notions of entropy and complexity, designed to measure, to some extent, the complexity of such optimization problems. We show that the notion of entropy is critically connected to the Universality Conjecture; for instance, that if the entropy grows at most exponentially with respect to [math], then the optimal constants of the [math]-linear Bohnenblust–Hille inequality for real scalars are indeed bounded universally with respect to [math]. It is likely that indeed the entropy grows as [math], and in this scenario, we show that the optimal constants are precisely [math]. In the bilinear case, [math], we show that any extremum of the Littlewood’s [math] inequality has entropy [math] and complexity [math], and thus we are able to classify all extrema of the problem. We also prove that, for any mixed [math]-Littlewood inequality, the entropy do grow exponentially and the sharp constants for such a class of inequalities are precisely [math]. In addition to the notions of entropy and complexity, the approach we develop in this work makes decisive use of a family of strongly non-symmetric [math]-linear forms, which has further consequences to the theory, as we explain herein. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:56Z DOI: 10.1142/S0219199717500298

Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we study an evolution equation involving the normalized [math]-Laplacian and a bounded continuous source term. The normalized [math]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [math] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:56Z DOI: 10.1142/S0219199717500353

Abstract: Communications in Contemporary Mathematics, Ahead of Print. We classify real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadrics [math], [math]. We show that [math] is even, say [math], and any such hypersurface becomes an open part of a tube around a [math]-dimensional complex hyperbolic space [math] which is embedded canonically in [math] as a totally geodesic complex submanifold or a horosphere whose center at infinity is [math]-isotropic singular. As a consequence of the result, we get the nonexistence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex quadrics [math], [math]. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:54Z DOI: 10.1142/S0219199717500316

Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we derive the following Leray–Trudinger type inequality on a bounded domain [math] in [math] containing the origin. supu∈W01,n(Ω),In[u,Ω,R]≤1∫Ωecn u(x) E2β x R n n−1dx < +∞, for some cn > 0 depending only on n. Here, [math], [math], [math] and [math], [math] for [math] This improves an earlier result by Psaradakis and Spector. Also, we prove that for any [math] in the place of [math], the above inequality is false if we take [math]. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:52Z DOI: 10.1142/S0219199717500341

Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math] be an integer. For any open domain [math], non-positive function [math] such that [math], and bounded sequence [math] we prove the existence of a sequence of functions [math] solving the Liouville equation of order [math] (−Δ)mu k = Vke2mukin Ω,limsupk→∞∫Ωe2mukdx < ∞, and blowing up exactly on the set [math], i.e. limk→∞uk(x) = +∞ for x ∈ Sφandlimk→∞uk(x) = −∞ for x ∈ Ω ∖ Sφ, thus showing that a result of Adimurthi, Robert and Struwe is sharp. We extend this result to the boundary of [math] and to the case [math]. Several related problems remain open. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:52Z DOI: 10.1142/S0219199717500262

Abstract: Communications in Contemporary Mathematics, Ahead of Print. The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for [math], where [math] is the base matrix and [math] is sampled from the GOE or the GUE random matrix ensembles. We bound the mean number of eigenvalues of [math] in an interval, and present tail bounds for the distribution of the Frobenius and operator norms of [math] and for the distribution of the norm of [math] applied to a fixed vector. The bounds are uniform in [math] and exceed the actual suprema by no more than multiplicative constants. The probability of multiple eigenvalues in an interval is also estimated. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:50Z DOI: 10.1142/S0219199717500286

Abstract: Communications in Contemporary Mathematics, Ahead of Print. We consider local weak solutions of the Poisson equation for the [math]-Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:49Z DOI: 10.1142/S0219199717500304

Abstract: Communications in Contemporary Mathematics, Ahead of Print. It has been recently shown by Meng and Zhang that the full automorphism group [math] is a Jordan group for all projective varieties in arbitrary dimensions. The aim of this paper is to show that the full automorphism group [math] is, in fact, a Jordan group even for all normal compact Kähler varieties in arbitrary dimensions. The meromorphic structure of the identity component of the automorphism group and its Rosenlicht-type decomposition play crucial roles in the proof. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:48Z DOI: 10.1142/S0219199717500249

Abstract: Communications in Contemporary Mathematics, Ahead of Print. The complete characterization of the phase portraits of real planar quadratic vector fields is very far from being accomplished. As it is almost impossible to work directly with the whole class of quadratic vector fields because it depends on twelve parameters, we reduce the number of parameters to five by using the action of the group of real affine transformations and time rescaling on the class of real quadratic differential systems. Using this group action, we obtain normal forms for the class of quadratic systems that we want to study with at most five parameters. Then working with these normal forms, we complete the characterization of the phase portraits in the Poincaré disc of all planar quadratic polynomial differential systems having an invariant conic [math]: [math], and a Darboux invariant of the form [math] with [math]. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:47Z DOI: 10.1142/S021919971750033X

Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: (−Δ)αu = f(x,u,v,∇u,∇v)in Ω,(−Δ)αv = g(x,u,v,∇u,∇v)in Ω,u = v = 0 in ℝN∖Ω, where [math] denotes the fractional Laplacian and [math] is a smooth bounded domain in [math]. It shown that under some assumptions on [math] and [math], the problem has at least one positive solution [math]. Our proof is based on the classical scaling method of Gidas and Spruck and topological degree theory. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:45Z DOI: 10.1142/S0219199717500328

Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math] and [math] be the local Hardy space in the sense of D. Goldberg. In this paper, the authors establish two bilinear decompositions of the product spaces of [math] and their dual spaces. More precisely, the authors prove that [math] and, for any [math], [math], where [math] denotes the local BMO space, [math], for any [math] and [math], the inhomogeneous Lipschitz space and [math] a variant of the local Orlicz–Hardy space related to the Orlicz function [math] for any [math] which was introduced by Bonami and Feuto. As an application, the authors establish a div-curl lemma at the endpoint case. Citation: Communications in Contemporary Mathematics PubDate: 2017-02-17T08:12:44Z DOI: 10.1142/S0219199717500250

Authors:Kanishka Perera, Marco Squassina Abstract: Communications in Contemporary Mathematics, Ahead of Print. We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero. Citation: Communications in Contemporary Mathematics PubDate: 2017-01-17T11:17:52Z DOI: 10.1142/S0219199717500237

Authors:Filomena Pacella, Michael Plum, Dagmar Rütters Abstract: Communications in Contemporary Mathematics, Ahead of Print. We prove existence, non-degeneracy, and exponential decay at infinity of a non-trivial solution to Emden’s equation [math] on an unbounded [math]-shaped domain, subject to Dirichlet boundary conditions. Besides the direct value of this result, we also regard this solution as a building block for solutions on expanding bounded domains with corners, to be established in future work. Our proof makes heavy use of computer assistance. Starting from a numerical approximate solution, we use a fixed-point argument to prove existence of a near-by exact solution. The eigenvalue bounds established in the course of this proof also imply non-degeneracy of the solution. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:53Z DOI: 10.1142/S0219199717500055

Authors:Manassés de Souza, Yane Lísley Araújo Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we study a class of fractional Schrödinger equations in [math] of the form (−Δ)αu + V (x)u = u 2α∗−2u + g(x,u), where [math], [math], [math] is the critical Sobolev exponent, [math] is a positive potential bounded away from zero, and the nonlinearity [math] behaves like [math] at infinity for some [math], and does not satisfy the usual Ambrosetti–Rabinowitz condition. We also assume that the potential [math] and the nonlinearity [math] are asymptotically periodic at infinity. We prove the existence of at least one solution [math] by combining a version of the mountain-pass theorem and a result due to Lions for critical growth. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:53Z DOI: 10.1142/S0219199717500110

Authors:Fabio Cavalletti, Andrea Mondino Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper we prove that in a metric measure space [math] verifying the measure contraction property with parameters [math] and [math], any optimal transference plan between two marginal measures is induced by an optimal map, provided the first marginal is absolutely continuous with respect to [math] and the space itself is essentially non-branching. In particular this shows that there exists a unique transport plan and it is induced by a map. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:52Z DOI: 10.1142/S0219199717500079

Authors:Qiang Fu Abstract: Communications in Contemporary Mathematics, Ahead of Print. In 1990, Beilinson–Lusztig–MacPherson (BLM) discovered a realization for quantum [math] via a geometric setting of quantum Schur algebras. We will generalize their result to the classical affine case. More precisely, we first use Ringel–Hall algebras to construct an integral form [math] of [math], where [math] is the universal enveloping algebra of the loop algebra [math]. We then establish the stabilization property of multiplication for the classical affine Schur algebras. This stabilization property leads to the BLM realization of [math] and [math]. In particular, we conclude that [math] is a [math]-Hopf subalgebra of [math]. As a bonus, this method leads to an explicit [math]-basis for [math], and it yields explicit multiplication formulas between generators and basis elements for [math]. As an application, we will prove that the natural algebra homomorphism from [math] to the affine Schur algebra over [math] is surjective. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:52Z DOI: 10.1142/S0219199717500134

Authors:Ulrich Kohlenbach, Laurenţiu Leuştean, Adriana Nicolae Abstract: Communications in Contemporary Mathematics, Ahead of Print. We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejér monotonicity where the convergence uses the compactness of the underlying set. These quantitative versions are in the form of explicit rates of so-called metastability in the sense of Tao. Our approach covers examples ranging from the proximal point algorithm for maximal monotone operators to various fixed point iterations [math] for firmly nonexpansive, asymptotically nonexpansive, strictly pseudo-contractive and other types of mappings. Many of the results hold in a general metric setting with some convexity structure added (so-called [math]-hyperbolic spaces). Sometimes uniform convexity is assumed still covering the important class of CAT(0)-spaces due to Gromov. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:51Z DOI: 10.1142/S0219199717500158

Authors:Alberto Boscaggin, Guglielmo Feltrin Abstract: Communications in Contemporary Mathematics, Ahead of Print. We prove that the superlinear indefinite equation u″ + a(t)up = 0, where [math] and [math] is a [math]-periodic sign-changing function satisfying the (sharp) mean value condition [math], has positive subharmonic solutions of order [math] for any large integer [math], thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it). Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:51Z DOI: 10.1142/S0219199717500213

Authors:Andrzej Weber, Michał Wojciechowski Abstract: Communications in Contemporary Mathematics, Ahead of Print. We consider Auerbach bases in Banach spaces of dimension [math]. We show that there exist at least [math] such bases. This estimate follows from the calculation of the Lusternik–Schnirelmann category of the flag variety. A better estimate is obtained for generic smooth Banach spaces using Morse theory. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:51Z DOI: 10.1142/S021919971750016X

Authors:Tingzhi Cheng, Genggeng Huang, Congming Li Abstract: Communications in Contemporary Mathematics, Ahead of Print. This paper is devoted to investigate the symmetry and monotonicity properties for positive solutions of fractional Laplacian equations. Especially, we consider the following fractional Laplacian equation with homogeneous Dirichlet condition: (−Δ)α 2u = f(x,u,∇u)in Ω, for α ∈ (0, 2).u > 0,in Ω; u ≡ 0,in ℝn∖Ω, Here [math] is a domain (bounded or unbounded) in [math] which is convex in [math]-direction. [math] is the nonlocal fractional Laplacian operator which is defined as (−Δ)α 2u(x) = Cn,αP.V.∫ℝnu(x) − u(y) x − y n+α , 0 < α < 2. Under various conditions on [math] and on a solution [math] it is shown that [math] is strictly increasing in [math] in the left half of [math], or in [math]. Symmetry (in [math]) of some solutions is proved. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:50Z DOI: 10.1142/S0219199717500183

Authors:Denis Borisov, Francisco Hoecker-Escuti, Ivan Veselić Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the spectrum of random ergodic Schrödinger-type operators in the weak disorder regime. We give upper and lower bounds on how much the spectrum expands at its bottom for very general perturbations. The background operator is assumed to be a periodic elliptic differential operator on [math], not necessarily of second order. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:50Z DOI: 10.1142/S0219199717500080

Authors:Nam Q. Le Abstract: Communications in Contemporary Mathematics, Ahead of Print. We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations. Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:50Z DOI: 10.1142/S0219199717500122

Authors:Dominic Breit, Bianca Stroffolini, Anna Verde Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study nonlinear parabolic Stokes systems with an asymptotically linear structure. This refers to the slow flow of a non-Newtonian fluid with Newtonian behavior for large shear rates. We show that the symmetric gradient of the velocity field is locally bounded in space-time. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:49Z DOI: 10.1142/S0219199717500067

Authors:Michael Ruzhansky, Durvudkhan Suragan Abstract: Communications in Contemporary Mathematics, Ahead of Print. We establish sharp remainder terms of the [math]-Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups, yielding the inequalities with best constants. Our methods also give new sharp Caffarelli–Kohn–Nirenberg-type inequalities in [math] with arbitrary quasi-norms. We also present explicit examples to illustrate our results for different weights and in abelian cases. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:49Z DOI: 10.1142/S0219199717500146

Authors:Paola Cavaliere, Andrea Cianchi, Luboš Pick, Lenka Slavíková Abstract: Communications in Contemporary Mathematics, Ahead of Print. A version of the Lebesgue differentiation theorem is offered, where the [math] norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation theorem are established. In particular, Lorentz, Orlicz and other customary norms for which Lebesgue’s theorem holds are characterized. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:48Z DOI: 10.1142/S0219199717500201

Authors:E. H. Gomes Tavares, M. A. Jorge Silva, T. F. Ma Abstract: Communications in Contemporary Mathematics, Ahead of Print. This paper is concerned with uniform stability of the energy corresponding to a class of nonlinear plate equations with memory. It is assumed that the memory kernel [math] satisfies the condition [math] of Alabau-Boussouira and Cannarsa [A general method for proving sharp energy decay rates for memory-dissipative evolution equations, C. R. Acad. Sci. Paris Ser. I 347 (2009) 867–872], where [math] is positive, convex, increasing, and satisfies [math]. Then, we obtain sharp energy decay rate in the sense that it recovers the decay rate assumed to the memory kernel. To this end we use a recent approach proposed by Lasiecka and Wang [Intrinsic decay rate estimates for semilinear abstract second order equations with memory, in New Prospects in Direct, Inverse and Control Problems for Evolution Equations, Springer Series INDAM, Vol. 10 (Series, 2014), pp. 271–303]. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:48Z DOI: 10.1142/S0219199717500109

Authors:Carlo Gasparetto, Filippo Gazzola Abstract: Communications in Contemporary Mathematics, Ahead of Print. We consider a class of Hill equations where the periodic coefficient is the squared solution of some Duffing equation plus a constant. We study the stability of the trivial solution of this Hill equation and we show that a criterion due to Burdina [Boundedness of solutions of a system of differential equations, Dokl. Akad. Nauk. SSSR 92 (1953) 603–606] is very helpful for this analysis. In some cases, we are also able to determine exact solutions in terms of Jacobi elliptic functions. Overall, we obtain a fairly complete picture of the stability and instability regions. These results are then used to study the stability of nonlinear modes in some beam equations. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:48Z DOI: 10.1142/S0219199717500225

Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the moduli space of rank 0 semistable sheaves on some rational surfaces. We show the irreducibility and stable rationality of them under some conditions. We also compute several (virtual) Betti numbers of those moduli spaces by computing their motivic measures. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:47Z DOI: 10.1142/S0219199717500195

Authors:Weiming Liu, Miaomiao Niu Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we study the existence of positive multi-peak solutions to the fractional Schrödinger–Poisson system ϵ2s(−Δ)su + V (x)u + Φ(x)u = up,x ∈ ℝ3, (−Δ)tΦ = u2, u > 0, x ∈ ℝ3, where [math] is a small parameter, [math] is a positive function, [math] and [math] Under some given conditions which are given in Sec. 1, we prove the existence of a positive solution with m-peaks and concentrating near a given local maximum point of [math] Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:47Z DOI: 10.1142/S0219199717500171

Authors:N. V. Krylov Abstract: Communications in Contemporary Mathematics, Ahead of Print. We establish the existence of solutions of fully nonlinear elliptic second-order equations like [math] in smooth domains without requiring [math] to be convex or concave with respect to the second-order derivatives. Apart from ellipticity nothing is required of [math] at points at which [math], where [math] is any given constant. For large [math] some kind of relaxed convexity assumption with respect to [math] mixed with a VMO condition with respect to [math] are still imposed. The solutions are sought in Sobolev classes. We also establish the solvability without almost any conditions on [math], apart from ellipticity, but of a “cut-off” version of the equation [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-12-22T07:33:47Z DOI: 10.1142/S0219199717500092

Authors:Armin Schikorra, Tien-Tsan Shieh, Daniel E. Spector Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this note we consider regularity theory for a fractional [math]-Laplace operator which arises in the complex interpolation of the Sobolev spaces, the [math]-Laplacian. We obtain the natural analogue to the classical [math]-Laplacian situation, namely [math]-regularity for the homogeneous equation. Citation: Communications in Contemporary Mathematics PubDate: 2016-10-19T10:06:08Z DOI: 10.1142/S0219199717500031

Authors:Debora Impera, Michele Rimoldi Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we obtain rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. Our approach relies on the theory of [math]-minimal hypersurfaces. Citation: Communications in Contemporary Mathematics PubDate: 2016-10-19T10:06:06Z DOI: 10.1142/S021919971750002X

Authors:Giulio Ciraolo, Luigi Vezzoni Abstract: Communications in Contemporary Mathematics, Ahead of Print. We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin’s overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere. Citation: Communications in Contemporary Mathematics PubDate: 2016-10-19T10:06:05Z DOI: 10.1142/S0219199717500018

Authors:M. Ceballos, J. Núñez, Á. F. Tenorio Abstract: Communications in Contemporary Mathematics, Ahead of Print. Given a finite-dimensional Leibniz algebra with certain basis, we show how to associate such algebra with a combinatorial structure of dimension 2. In some particular cases, this structure can be reduced to a digraph or a pseudodigraph. In this paper, we study some theoretical properties about this association and we determine the type of Leibniz algebra associated to each of them. Citation: Communications in Contemporary Mathematics PubDate: 2016-10-19T10:05:52Z DOI: 10.1142/S0219199717500043

Authors:Luigi C. Berselli, Stefano Spirito Abstract: Communications in Contemporary Mathematics, Ahead of Print. We prove that suitable weak solutions of 3D Navier–Stokes equations in bounded domains can be constructed by a particular type of artificial compressibility approximation. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:30:01Z DOI: 10.1142/S0219199716500644

Authors:Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Abstract: Communications in Contemporary Mathematics, Ahead of Print. Sharpened forms of the concentration of measure phenomenon for classes of functions on the sphere are developed in terms of Hessians of these functions. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:30:00Z DOI: 10.1142/S0219199716500589

Authors:Carlos E. Arreche Abstract: Communications in Contemporary Mathematics, Ahead of Print. We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation [math] where the coefficients [math] are rational functions in [math] with coefficients in [math]. We develop algorithms to compute the difference-differential Galois group associated to such an equation, and show how to deduce the differential-algebraic relations among the solutions from the defining equations of the Galois group. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:30:00Z DOI: 10.1142/S0219199716500565

Authors:Sun-Sig Byun, Yunsoo Jang Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study homogenization of the conormal derivative problem for an elliptic system with discontinuous coefficients in a bounded domain. A uniform global [math] estimate for [math] is obtained under optimal assumptions that the coefficients have a small bounded mean oscillation (BMO) seminorm and the domain is a [math]-Reifenberg flat domain whose boundary might be fractal. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:59Z DOI: 10.1142/S0219199716500620

Authors:S. Prashanth, Sweta Tiwari, K. Sreenadh Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we consider the following singular elliptic problem involving an exponential nonlinearity in two dimensions: −Δu = u−δ + λup+1euβ,u > 0 in Ω, u = 0on ∂Ω, where [math] is a bounded domain with smooth boundary, [math], [math], [math] and [math]. We show the existence and multiplicity of positive solutions globally with respect to the bifurcation parameter [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:58Z DOI: 10.1142/S021919971650067X

Authors:César R. de Oliveira, Alessandra A. Verri Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the operator [math] restricted to a waveguide [math], with heterogeneous function [math] constant in the longitudinal direction. The purpose is to obtain an effective operator, in the norm resolvent sense, when the diameter of [math] tends to zero with heterogeneity approaching a homogeneous situation (i.e. a constant function [math]). The effective operator presents a potential that, besides the traditional dependence on waveguide geometric properties, there is also a contribution from [math] which results, when combined with the curvature, for example, in the possibility of a repulsive interaction. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:58Z DOI: 10.1142/S0219199716500607

Authors:Gennaro Di Brino, Luca F. Di Cerbo Abstract: Communications in Contemporary Mathematics, Ahead of Print. We apply the recent results of Galkin et al. [Derived categories of Keum's fake projective planes, Adv. Math. 278 (2015) 238–253] to study some geometrical features of Keum's fake projective planes. Among other things, we show that the bicanonical map of Keum's fake projective planes is always an embedding. Moreover, we construct a nonstandard exceptional collection on the unique fake projective plane [math] with [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:56Z DOI: 10.1142/S0219199716500668

Authors:Shiri Artstein-Avidan, Boaz A. Slomka Abstract: Communications in Contemporary Mathematics, Ahead of Print. The fundamental theorem of affine geometry is a classical and useful result. For finite-dimensional real vector spaces, the theorem roughly states that a bijective self-mapping which maps lines to lines is affine-linear. In this paper, we prove several generalizations of this result and of its classical projective counterpart. We show that under a significant geometric relaxation of the hypotheses, namely that only lines parallel to one of a fixed set of finitely many directions are mapped to lines, an injective mapping of the space must be of a very restricted polynomial form. We also prove that under mild additional conditions the mapping is forced to be affine-additive or affine-linear. For example, we show that five directions in three-dimensional real space suffice to conclude affine-additivity. In the projective setting, we show that [math] fixed projective points in real [math]-dimensional projective space, through which all projective lines that pass are mapped to projective lines, suffice to conclude projective-linearity. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:55Z DOI: 10.1142/S0219199716500590

Authors:Xiaodong Wang Abstract: Communications in Contemporary Mathematics, Ahead of Print. We establish an integral formula on a smooth, precompact domain in a Kähler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula, we also prove some geometric inequalities when the boundary has positive Hermitian mean curvature. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:54Z DOI: 10.1142/S0219199716500632

Authors:Kōdai Fujimoto, Naoto Yamaoka Abstract: Communications in Contemporary Mathematics, Ahead of Print. This paper deals with an equivalent system to the nonlinear differential equation of Liénard type [math], where the range of the function [math] is bounded. Sufficient conditions are obtained for the system to have at least one limit cycle. The proofs of our results are based on phase plane analysis of the system with the Poincaré–Bendixon theorem. Moreover, to show that these sufficient conditions are suitable in some sense, we also establish the results that the system has no limit cycles. Finally, some examples are given to illustrate our results. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:53Z DOI: 10.1142/S0219199716500577

Authors:Weiren Zhao Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we prove the local existence and uniqueness of the solution with discontinuous density for the inhomogeneous non-resistive magnetohydrodynamics (MHD) equations on a [math] bounded domain [math] or [math], if the initial data [math] with [math] satisfies [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:52Z DOI: 10.1142/S0219199716500553

Authors:Daniel Hug, Rolf Schneider Abstract: Communications in Contemporary Mathematics, Ahead of Print. For valuations on convex bodies in Euclidean spaces, there is by now a long series of characterization and classification theorems. The classical template is Hadwiger’s theorem, saying that every rigid motion invariant, continuous, real-valued valuation on convex bodies in [math] is a linear combination of the intrinsic volumes. For tensor-valued valuations, under the assumptions of isometry covariance and continuity, there is a similar classification theorem, due to Alesker. Also for the local extensions of the intrinsic volumes, the support, curvature and area measures, there are analogous characterization results, with continuity replaced by weak continuity, and involving an additional assumption of local determination. The present authors have recently obtained a corresponding characterization result for local tensor valuations, or tensor-valued support measures (generalized curvature measures), of convex bodies in [math]. The covariance assumed there was with respect to the group [math] of orthogonal transformations. This was suggested by Alesker’s observation, according to which in dimensions [math], the weaker assumption of [math] covariance does not yield more tensor valuations. However, for tensor-valued support measures, the distinction between proper and improper rotations does make a difference. This paper considers, therefore, the local tensor valuations sharing the previously assumed properties, but with [math] covariance replaced by [math] covariance, and provides a complete classification. New tensor-valued support measures appear only in dimensions 2 and 3. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:51Z DOI: 10.1142/S0219199716500619

Authors:Shiguang Ma Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we introduce a nonlinear ODE method to construct constant mean curvature (CMC) surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like [math]. The existence of unstable CMC spheres tells us that the stability condition in Qing–Tian’s work [On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds, J. Amer. Math. Soc. 20(4) (2007) 1091–1110] cannot be removed generally. Citation: Communications in Contemporary Mathematics PubDate: 2016-08-18T07:29:50Z DOI: 10.1142/S0219199716500656

Authors:Ping Li Abstract: Communications in Contemporary Mathematics, Ahead of Print. The Hirzebruch [math]-genus and Poincaré polynomial share some similar features. In this paper, we investigate two of their similar features simultaneously. Through this process we shall derive several new results as well as reprove and improve some known results. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:17Z DOI: 10.1142/S0219199716500486

Authors:Marcelo M. Disconzi, David G. Ebin Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of the initial velocity of the compressible flow at time zero is assumed to be small. Furthermore, we find that solutions to the compressible motion problem in Lagrangian coordinates depend differentiably on their initial data, an unexpected result for this type of nonlinear equations. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:16Z DOI: 10.1142/S0219199716500541

Authors:The Anh Bui, Xuan Truong Le Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we prove the global gradient estimates on the generalized Lebesgue spaces for weak solutions to elliptic quasilinear obstacle problems. It is worth noticing that the coefficients related to the obstacle problems are merely measurable with small BMO norms and the underlying domain does not satisfy any smoothness conditions. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:15Z DOI: 10.1142/S0219199716500462

Authors:Amandine Aftalion, Christos Sourdis Abstract: Communications in Contemporary Mathematics, Ahead of Print. This paper deals with the study of the behavior of the wave functions of a two-component Bose–Einstein condensate near the interface, in the case of strong segregation. This yields a system of two coupled ordinary differential equations for which we want to have estimates on the asymptotic behavior, as the strength of the coupling tends to infinity. As in phase separation models, the leading order profile is a hyperbolic tangent. We construct an approximate solution and use the properties of the associated linearized operator to perturb it into a genuine solution for which we have an asymptotic expansion. We prove that the constructed heteroclinic solutions are linearly nondegenerate, in the natural sense, and that there is a spectral gap, independent of the large interaction parameter, between the zero eigenvalue (due to translations) at the bottom of the spectrum and the rest of the spectrum. Moreover, we prove a uniqueness result which implies that, in fact, the constructed heteroclinic is the unique minimizer (modulo translations) of the associated energy, for which we provide an expansion. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:14Z DOI: 10.1142/S0219199716500528

Authors:Patricia Cahn Abstract: Communications in Contemporary Mathematics, Ahead of Print. Previously we defined an operation [math] that generalizes Turaev’s cobracket for loops on a surface. We showed that, in contrast to the cobracket, this operation gives a formula for the minimum number of self-intersections of a loop in a given free homotopy class. In this paper, we consider the corresponding question for virtual strings, and conjecture that [math] gives a formula for the minimum number of self-intersection points of a virtual string in a given virtual homotopy class. To support the conjecture, we show that [math] gives a bound on the minimal self-intersection number of a virtual string which is stronger than a bound given by Turaev’s virtual string cobracket. We also use Turaev’s based matrices to describe a large set of strings [math] such that [math] gives a formula for the minimal self-intersection number [math]. Finally, we compare the bound given by [math] to a bound given by Turaev’s based matrix invariant [math], and construct an example that shows the bound on the minimal self-intersection number given by [math] is sometimes stronger than the bound [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:13Z DOI: 10.1142/S021919971650053X

Authors:M. L. M. Carvalho, Edcarlos D. da Silva, C. Goulart Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, the existence and multiplicity of solutions for a quasilinear elliptic problem driven by the [math]-Laplacian operator is established. These solutions are also built as ground state solutions using the Nehari method. The main difficulty arises from the fact that the [math]-Laplacian operator is not homogeneous and the nonlinear term is indefinite. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:13Z DOI: 10.1142/S0219199716500504

Authors:Minghua Lin Abstract: Communications in Contemporary Mathematics, Ahead of Print. In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality det(A2 + BA ) ≤det(A2 + AB), where [math] are [math] positive semidefinite matrices. We complement his result by proving det(A2 + AB ) ≥det(A2 + AB). Our proofs feature the fruitful interplay between determinantal inequalities and majorization relations. Some related questions are mentioned. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:13Z DOI: 10.1142/S0219199716500449

Authors:Xiaole Su, Hongwei Sun, Yusheng Wang Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we give some generalized packing radius theorems of an [math]-dimensional Alexandrov space [math] with curvature [math]. Let [math] be any [math]-separated subset in [math] (i.e. the distance [math] for any [math]). Under the condition “[math]” (after [K. Grove and F. Wilhelm, Hard and soft packing radius theorems, Ann. of Math.142 (1995) 213–237]), we give the upper bound of [math] (which depends only on [math]), and classify the geometric structure of [math] when [math] attains the upper bound. As a corollary, we get an isometrical sphere theorem in Riemannian case. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:12Z DOI: 10.1142/S0219199716500498

Authors:Ederson Moreira dos Santos, Filomena Pacella Abstract: Communications in Contemporary Mathematics, Ahead of Print. We consider non-autonomous semilinear elliptic equations of the type −Δu = x αf(u),x ∈ Ω,u = 0 on ∂Ω, where [math] is either a ball or an annulus centered at the origin, [math] and [math] is [math] on bounded sets of [math]. We address the question of estimating the Morse index [math] of a sign changing radial solution [math]. We prove that [math] for every [math] and that [math] if [math] is even. If [math] is superlinear the previous estimates become [math] and [math], respectively, where [math] denotes the number of nodal sets of [math], i.e. of connected components of [math]. Consequently, every least energy nodal solution [math] is not radially symmetric and [math] as [math] along the sequence of even exponents [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:12Z DOI: 10.1142/S0219199716500425

Authors:Joachim Kock, David I. Spivak Abstract: Communications in Contemporary Mathematics, Ahead of Print. It is well known that the category of finite sets and cospans, composed by pushout, contains the universal special commutative Frobenius algebra. In this paper, we observe that the same construction yields also general commutative Frobenius algebras, if just the pushouts are changed to homotopy pushouts. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:08Z DOI: 10.1142/S0219199716500474

Authors:Huyuan Chen, Guangying Lv Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math], [math] be a bounded open domain in [math] ([math]) with a [math] boundary [math] and [math] be a Hausdorff measure on [math]. We denote by [math] 〈ωα,f〉 =∫∂Ω∂αf(x) ∂n→xα dω(x),∀f ∈ Cα(Ω̄), where [math] is the unit inward normal vector of [math] at point [math] and ∂αf(x) ∂n→xα =limt→0+ f(x + tn→x) − f(x) tα . Our purpose of this paper is to study a nonlocal elliptic problem involving gradient nonlinearity (−Δ)αu = g( ∇u ) + kω αin Ω̄, u = 0 in ℝN\Ω̄, where [math], the operator [math] is the fractional Laplacian and [math] is a locally Hölder continuous function satisfying some extra condition. We show that the above problem admits a nonnegative weak solution [math], which is a classical solution of (−Δ)αu = g( ∇u ) in Ω, u = 0 in ℝN\Ω̄, limx∈Ω,x→∂Ωu(x) = +∞. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:07Z DOI: 10.1142/S0219199716500516

Authors:Meng Wang Abstract: Communications in Contemporary Mathematics, Ahead of Print. The fractional Yamabe problem was proposed by González and Qing in [Fractional conformal Laplacians and fractional Yamabe problems, Anal. PDE 6(7) (2013) 1535–1576]. One of their results is that if the fractional Yamabe constant satisfies [math], then the fractional Yamabe problem is solvable for [math]. Using the method from Brezis–Lieb, we give a new, and shorter proof, of this statement. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:07Z DOI: 10.1142/S0219199716500450

Authors:Hua Chen, Shuying Tian, Yawei Wei Abstract: Communications in Contemporary Mathematics, Ahead of Print. The present paper is concern with the Dirichlet problem for semi-linear corner degenerate elliptic equations with singular potential term. We first give the preliminary of the framework and then discuss the weighted corner type Hardy inequality. By using the variational method, we prove the existence of multiple solutions for the Dirichlet boundary-value problem. Citation: Communications in Contemporary Mathematics PubDate: 2016-06-14T08:33:06Z DOI: 10.1142/S0219199716500437

Authors:Yunhe Sheng, Chenchang Zhu Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The extension results in a higher Lie algebroid. We give exact Courant algebroids and string Lie 2-algebras as examples of such extensions. We then apply this to obtain a Lie 2-groupoid integrating an exact Courant algebroid. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:27Z DOI: 10.1142/S0219199716500346

Authors:Ben Cox, Xiangqian Guo, Rencai Lu, Kaiming Zhao Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math], [math]. Then we have the algebraic curve [math], and its coordinate algebras (the Riemann surfaces) [math] and [math] The Lie algebras [math] and [math] are called the [math]th superelliptic Lie algebras associated to [math]. In this paper, we determine the necessary and sufficient conditions for such Lie algebras to be simple, and determine their universal central extensions and their derivation algebras. We also study the isomorphism and automorphism problem for these Lie algebras, which will help to understand the birational equivalence of some algebraic curves of the form [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:26Z DOI: 10.1142/S0219199716500322

Authors:Agnès Gadbled, Anne-Laure Thiel, Emmanuel Wagner Abstract: Communications in Contemporary Mathematics, Ahead of Print. Using a quiver algebra of a double cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:26Z DOI: 10.1142/S0219199716500243

Authors:Petru Jebelean, Jean Mawhin, Călin Şerban Abstract: Communications in Contemporary Mathematics, Ahead of Print. We prove the existence of at least [math] geometrically distinct [math]-periodic solutions for a differential inclusions system of the form −(ψ(u′))′∈ ∂F(t,u) + h(t). Here, [math] is a monotone homeomorphism, [math] is periodic with respect to each component of the second variable and [math] stands for the generalized Clarke gradient of [math] at [math]. The monotonicity assumptions on [math] highlight the vector [math]-Laplacian as being the prototype differential operator. The main interesting feature of this approach is that it also provides a useful framework to treat the case of the [math]-relativistic singular operator. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:25Z DOI: 10.1142/S0219199716500292

Authors:Luminiţa Barbu, Gheorghe Moroşanu Abstract: Communications in Contemporary Mathematics, Ahead of Print. Consider in a Hilbert space [math] the Cauchy problem [math]: [math], and associate with it the second-order problem [math]: [math], where [math] is a (possibly set-valued) maximal monotone operator, [math] is a Lipschitz operator, and [math] is a positive small parameter. Note that [math] is an elliptic-like regularization of [math] in the sense suggested by Lions in his book on singular perturbations. We prove that the solution [math] of [math] approximates the solution [math] of [math]: [math]. Applications to the nonlinear heat equation as well as to the nonlinear telegraph system and the nonlinear wave equation are presented. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:25Z DOI: 10.1142/S0219199716500371

Authors:Indranil Chowdhury, Prosenjit Roy Abstract: Communications in Contemporary Mathematics, Ahead of Print. The paper is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second-order elliptic problems by Chipot and Rougirel in [On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math. 4(1) (2002) 15–44], where the force functions are considered on the cross-section of domains, we prove the non-local counterpart of their result. Recently in [Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89(1–2) (2014) 21–35] Yeressian established a weighted estimate for solutions of non-local Dirichlet problems which exhibit the asymptotic behavior. The case when [math] was also treated as an example to show how the weighted estimate might be used to achieve the asymptotic behavior. In this paper, we extend this result to each order between [math] and [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:24Z DOI: 10.1142/S0219199716500358

Authors:João Marcos Do Ó, Federica Sani, Cristina Tarsi Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math], [math] and [math]. Our aim is to clarify the influence of the constraint [math] on concentration phenomena of (spherically symmetric and non-increasing) maximizing sequences for the Trudinger–Moser supremum dN(a,b) :=supu∈Sa,b∫ℝNϕN(αN u N N−1)dx, where [math] is the sharp exponent of Moser, i.e. [math] and [math] is the surface measure of the [math]-dimensional unit sphere in [math]. We obtain a vanishing-concentration-compactness alternative showing that maximizing sequences for [math] cannot concentrate either when [math] or when [math] and [math] is sufficiently small. From this alternative, we deduce the attainability of [math] for special values of the parameters [math] and [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:24Z DOI: 10.1142/S021919971650036X

Authors:Feida Jiang, Ni Xiang, Jinju Xu Abstract: Communications in Contemporary Mathematics, Ahead of Print. This paper concerns the gradient estimates for Neumann problem of a certain Monge–Ampère type equation with a lower order symmetric matrix function in the determinant. Under a one-sided quadratic structure condition on the matrix function, we present two alternative full discussions of the global gradient bound for the elliptic solutions. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:24Z DOI: 10.1142/S0219199716500413

Authors:Andrea Colesanti, Daniel Hug, Eugenia Saorín Gómez Abstract: Communications in Contemporary Mathematics, Ahead of Print. For a broad class of integral functionals defined on the space of [math]-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn–Minkowski type inequality. In particular, we prove that a Brunn–Minkowski type inequality implies monotonicity, and that a general Brunn–Minkowski type inequality is equivalent to the functional being a mixed volume. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:23Z DOI: 10.1142/S0219199716500334

Authors:Rodrigo C. M. Nemer, Jefferson A. Santos Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this work, we study multiplicity of nontrivial solution for the following class of differential inclusion problems with nonhomogeneous Neumann condition through Orlicz–Sobolev spaces, −div(ϕ( ∇u )∇u) + ϕ( u )u ∈ λ∂F(u)in Ω,∂u ∂ν ∈ μ∂G(u)on ∂Ω, where [math] is a domain, [math] and [math] is the generalized gradient of [math]. The main tools used are Variational Methods for Locally Lipschitz Functional and Critical Point Theory. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:21Z DOI: 10.1142/S0219199716500310

Authors:Jianjun Zhang, João Marcos do Ó, Marco Squassina Abstract: Communications in Contemporary Mathematics, Ahead of Print. We consider a Schrödinger–Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti–Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:21Z DOI: 10.1142/S0219199716500280

Authors:Thierry Cazenave, Ivan Naumkin Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we construct for every [math] and [math] a class of initial values [math] for which there exists a local solution of the nonlinear Schrödinger equation [math] on [math] with the initial condition [math]. Moreover, we construct for every [math] a class of (arbitrarily large) initial values for which there exists a global solution that scatters as [math]. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:21Z DOI: 10.1142/S0219199716500383

Authors:Juan Pablo Pinasco, Ariel Martin Salort Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this work, we study the asymptotic behavior of the curves of the Fučík spectrum for weighted second-order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the spectrum in terms of some integrals of the weights. We present an algorithm which computes the intersection of the Fučík spectrum with rays through the origin, and we compare their values with the asymptotic ones. Citation: Communications in Contemporary Mathematics PubDate: 2016-05-13T07:37:21Z DOI: 10.1142/S0219199716500395

Authors:Anna-Louise Grensing, Volodymyr Mazorchuk Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study finitary [math]-categories associated to dual projection functors for finite-dimensional associative algebras. In the case of path algebras of admissible tree quivers (which includes all Dynkin quivers of type [math]), we show that the monoid generated by dual projection functors is the Hecke–Kiselman monoid of the underlying quiver and also obtain a presentation for the monoid of indecomposable subbimodules of the identity bimodule. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:49Z DOI: 10.1142/S0219199716500164

Authors:Benoît Vicedo, Charles Young Abstract: Communications in Contemporary Mathematics, Ahead of Print. Given a vertex Lie algebra [math] equipped with an action by automorphisms of a cyclic group [math], we define spaces of cyclotomic coinvariants over the Riemann sphere. These are quotients of tensor products of smooth modules over “local” Lie algebras [math] assigned to marked points [math], by the action of a “global” Lie algebra [math] of [math]-equivariant functions. On the other hand, the universal enveloping vertex algebra [math] of [math] is itself a vertex Lie algebra with an induced action of [math]. This gives “big” analogs of the Lie algebras above. From these we construct the space of “big” cyclotomic coinvariants, i.e. coinvariants with respect to [math]. We prove that these two definitions of cyclotomic coinvariants in fact coincide, provided the origin is included as a marked point. As a corollary, we prove a result on the functoriality of cyclotomic coinvariants which we require for the solution of cyclotomic Gaudin models in [B. Vicedo and C. Young, Cyclotomic Gaudin models: Construction and Bethe ansatz, preprint (2014); arXiv:1409.6937]. At the origin, which is fixed by [math], one must assign a module over the stable subalgebra [math] of [math]. This module becomes a [math]-quasi-module in the sense of Li. As a bi-product we obtain an iterate formula for such quasi-modules. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:48Z DOI: 10.1142/S0219199716500152

Authors:Mehmet Akif Akyol, Bayram Şahin Abstract: Communications in Contemporary Mathematics, Ahead of Print. As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which arise from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also check the harmonicity of such submersions and find necessary and sufficient conditions of a conformal semi-invariant submersion to be totally geodesic. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:48Z DOI: 10.1142/S0219199716500115

Authors:Jinwei Yang Abstract: Communications in Contemporary Mathematics, Ahead of Print. We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded vertex algebra under a certain finiteness condition and a condition related to the horizontal gradings. Using these systems of differential equations, we verify the convergence and extension property needed in the logarithmic tensor category theory for such strongly graded generalized modules developed by Huang, Lepowsky and Zhang. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:48Z DOI: 10.1142/S0219199716500097

Authors:Peter Hästö, Ana Margarida Ribeiro Abstract: Communications in Contemporary Mathematics, Ahead of Print. The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Since the difference quotient is based on shifting the function, it cannot be generalized to the variable exponent case. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the variable exponent Sobolev space. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:47Z DOI: 10.1142/S021919971650022X

Authors:David Arcoya, José Carmona, Pedro J. Martínez-Aparicio Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we are concerned with the zero Dirichlet boundary value problem associated to the quasilinear elliptic equation −div(a(u)M(x)∇u) + H(x,u,∇u) = f(x),x ∈ Ω, where [math] is an open and bounded set in [math] ([math]), [math] is a continuously differentiable real function in [math], [math] is an elliptic, bounded and symmetric matrix, [math] is non-negative and may be singular at zero and [math]. We give sufficient conditions on [math], [math] and [math] in order to have a comparison principle and, as a consequence, uniqueness of positive solutions being continuous up to the boundary. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:47Z DOI: 10.1142/S0219199716500139

Authors:Martin Kohls, Müfi̇t Sezer Abstract: Communications in Contemporary Mathematics, Ahead of Print. For a finite-dimensional representation [math] of a group [math] over a field [math], the degree of reductivity [math] is the smallest degree [math] such that every nonzero fixed point [math] can be separated from zero by a homogeneous invariant of degree at most [math]. We compute [math] explicitly for several classes of modular groups and representations. We also demonstrate that the maximal size of a cyclic subgroup is a sharp lower bound for this number in the case of modular abelian [math]-groups. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:47Z DOI: 10.1142/S0219199716500231

Authors:Mingzheng Sun, Jiabao Su, Hongrui Cai Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, by Morse theory, we study the existence and multiplicity of solutions for the [math]-Laplacian equation with a “concave” nonlinearity and a parameter. In our results, we do not need any additional global condition on the nonlinearities, except for a subcritical growth condition. Citation: Communications in Contemporary Mathematics PubDate: 2016-02-16T10:01:46Z DOI: 10.1142/S0219199716500140

Authors:Irene Benedetti, Nguyen Van Loi, Luisa Malaguti, Valeri Obukhovskii Abstract: Communications in Contemporary Mathematics, Ahead of Print. A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integro-differential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given. Citation: Communications in Contemporary Mathematics PubDate: 2016-01-04T08:05:39Z DOI: 10.1142/S0219199716500024

Authors:Simon Kapfer Abstract: Communications in Contemporary Mathematics, Ahead of Print. The Beauville–Fujiki relation for a compact Hyperkähler manifold [math] of dimension [math] allows to equip the symmetric power [math] with a symmetric bilinear form induced by the Beauville–Bogomolov form. We study some of its properties and compare it to the form given by the Poincaré pairing. The construction generalizes to a definition for an induced symmetric bilinear form on the symmetric power of any free module equipped with a symmetric bilinear form. We point out how the situation is related to the theory of orthogonal polynomials in several variables. Finally, we construct a basis of homogeneous polynomials that are orthogonal when integrated over the unit sphere [math], or equivalently, over [math] with a Gaussian kernel. Citation: Communications in Contemporary Mathematics PubDate: 2016-01-04T08:05:35Z DOI: 10.1142/S0219199716500073

Authors:Cristian Bereanu, Daniel de la Fuente, Alfonso Romero, Pedro J. Torres Abstract: Communications in Contemporary Mathematics, Ahead of Print. We provide sufficient conditions for the existence of a uniparametric family of entire spacelike graphs with prescribed mean curvature in a Friedmann–Lemaître–Robertson–Walker spacetime with flat fiber. The proof is based on the analysis of the associated homogeneous Dirichlet problem on a Euclidean ball together with suitable bounds for the gradient which permit the prolongability of the solution to the whole space. Citation: Communications in Contemporary Mathematics PubDate: 2016-01-04T08:05:34Z DOI: 10.1142/S0219199716500061