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MATHEMATICS (643 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 20)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 9)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 4)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access  
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Analysis & Computational Mathematics     Hybrid Journal   (Followers: 5)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 1)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Calculus of Variations and Partial Differential Equations
  [SJR: 2.455]   [H-I: 44]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0835 - ISSN (Online) 0944-2669
   Published by Springer-Verlag Homepage  [2335 journals]
  • Isoperimetry with upper mean curvature bounds and sharp stability
    • Authors: B. Krummel; F. Maggi
      Abstract: It was proved by Almgren that among boundaries whose mean curvature is bounded from above, perimeter is uniquely minimized by balls. We obtain sharp stability estimates for Almgren’s isoperimetric principle and, as an application, we deduce a sharp description of boundaries with almost constant mean curvature under a total perimeter bound which prevents bubbling.
      PubDate: 2017-03-24
      DOI: 10.1007/s00526-017-1139-3
      Issue No: Vol. 56, No. 2 (2017)
  • Infinitely many non-radial solutions for fractional Nirenberg problem
    • Authors: Chungen Liu; Qiang Ren
      Abstract: In this paper, the prescribed \(\sigma \) -curvature problem $$\begin{aligned} P_{\sigma }^{g_0} u={\tilde{K}}(x)u^{\frac{N+2\sigma }{N-2\sigma }}, x\in {\mathbb {S}}^N,u>0 \end{aligned}$$ is considered. When \({\tilde{K}}(x)\) is some axis symmetric function on \({\mathbb {S}}^N\) , by using singular perturbation method, it is proved that this problem possesses infinitely many non-radial solutions for \(0<\sigma \le 1\) and \(N> 2\sigma +2\) .
      PubDate: 2017-03-23
      DOI: 10.1007/s00526-017-1141-9
      Issue No: Vol. 56, No. 2 (2017)
  • Discreteness of interior transmission eigenvalues revisited
    • Authors: Hoai-Minh Nguyen; Quoc-Hung Nguyen
      Abstract: This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for which only the information near the boundary are required and there might be no contrast of the coefficients on the boundary.
      PubDate: 2017-03-22
      DOI: 10.1007/s00526-017-1143-7
      Issue No: Vol. 56, No. 2 (2017)
  • Regularity of $$\omega $$ ω -minimizers for a class of functionals with
           non-standard growth
    • Authors: Jihoon Ok
      Abstract: We prove local Hölder continuity results for \(\omega \) -minimizers of a class of functionals with non-standard growth, characterized by the fact of having a double type of degeneracy, and thereby extending to \(\omega \) -minimizers the results obtained in Colombo and Mingione (Arch Ration Mech Anal 215(2):443–496, 2015) for ordinary minimizers. As a side benefit of the proof, we also consider a class of functionals with Orlicz-growth and prove regularity for \(\omega \) -minimizers.
      PubDate: 2017-03-21
      DOI: 10.1007/s00526-017-1137-5
      Issue No: Vol. 56, No. 2 (2017)
  • On the p -Laplacian with Robin boundary conditions and boundary trace
    • Authors: Hynek Kovařík; Konstantin Pankrashkin
      Abstract: Let \(\Omega \subset \mathbb {R}^\nu \) , \(\nu \ge 2\) , be a \(C^{1,1}\) domain whose boundary \(\partial \Omega \) is either compact or behaves suitably at infinity. For \(p\in (1,\infty )\) and \(\alpha >0\) , define $$\begin{aligned} \Lambda (\Omega ,p,\alpha ):=\inf _{\begin{array}{c} u\in W^{1,p}(\Omega )\\ u\not \equiv 0 \end{array}}\dfrac{\displaystyle \int _\Omega \nabla u ^p \mathrm {d} x - \alpha \displaystyle \int _{\partial \Omega } u ^p\mathrm {d}\sigma }{\displaystyle \int _\Omega u ^p\mathrm {d} x}, \end{aligned}$$ where \(\mathrm {d}\sigma \) is the surface measure on \(\partial \Omega \) . We show the asymptotics $$\begin{aligned} \Lambda (\Omega ,p,\alpha )=-(p-1)\alpha ^{\frac{p}{p-1}} - (\nu -1)H_\mathrm {max}\, \alpha + o(\alpha ), \quad \alpha \rightarrow +\infty , \end{aligned}$$ where \(H_\mathrm {max}\) is the maximum mean curvature of \(\partial \Omega \) . The asymptotic behavior of the associated minimizers is discussed as well. The estimate is then applied to the study of the best constant in a boundary trace theorem for expanding domains, to the norm estimate for extension operators and to related isoperimetric inequalities.
      PubDate: 2017-03-21
      DOI: 10.1007/s00526-017-1138-4
      Issue No: Vol. 56, No. 2 (2017)
  • Estimates for the first eigenvalue of Jacobi operator on hypersurfaces
           with constant mean curvature in spheres
    • Authors: Daguang Chen; Qing-Ming Cheng
      Abstract: In this paper, we study the first eigenvalue of Jacobi operator on an n-dimensional non-totally umbilical compact hypersurface with constant mean curvature H in the unit sphere \(S^{n+1}(1)\) . We give an optimal upper bound for the first eigenvalue of Jacobi operator, which only depends on the mean curvature H and the dimension n. This bound is attained if and only if, \(\varphi :\ M \rightarrow S^{n+1}(1)\) is isometric to \(S^1(r)\times S^{n-1}(\sqrt{1-r^2})\) when \(H\ne 0\) or \(\varphi :\ M \rightarrow S^{n+1}(1)\) is isometric to a Clifford torus \( S^{n-k}\left( \sqrt{\dfrac{n-k}{n}}\right) \times S^k\left( \sqrt{\dfrac{k}{n}}\right) \) , for \(k=1, 2, \ldots , n-1\) when \(H=0\) .
      PubDate: 2017-03-21
      DOI: 10.1007/s00526-017-1132-x
      Issue No: Vol. 56, No. 2 (2017)
  • Global Lorentz estimates for nonlinear parabolic equations on nonsmooth
    • Authors: The Anh Bui; Xuan Thinh Duong
      Abstract: Consider the nonlinear parabolic equation in the form $$\begin{aligned} u_t-\mathrm{div}{\mathbf {a}}(D u,x,t)=\mathrm{div}\,( F ^{p-2}F) \quad \text {in} \quad \Omega \times (0,T), \end{aligned}$$ where \(T>0\) and \(\Omega \) is a Reifenberg domain. We suppose that the nonlinearity \({\mathbf {a}}(\xi ,x,t)\) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderón-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity \({\mathbf {a}}(\xi ,x,t)\) and to more general setting of Lorentz spaces.
      PubDate: 2017-03-20
      DOI: 10.1007/s00526-017-1130-z
      Issue No: Vol. 56, No. 2 (2017)
  • Stability of the traveling waves for the derivative Schrödinger
           equation in the energy space
    • Authors: Changxing Miao; Xingdong Tang; Guixiang Xu
      Abstract: In this paper, we continue the study of the dynamics of the traveling waves for nonlinear Schrödinger equation with derivative (DNLS) in the energy space. Under some technical assumptions on the speed of each traveling wave, the stability of the sum of two traveling waves for DNLS is obtained in the energy space by Martel–Merle–Tsai’s analytic approach in Martel et al. (Commun Math Phys 231(2):347–373, 2002, Duke Math J 133(3):405–466, 2006). As a by-product, we also give an alternative proof of the stability of the single traveling wave in the energy space in Colin and Ohta (Ann Inst Henri Poincaré Anal Non Linéaire 23(5):753–764, 2006), where Colin and Ohta made use of the concentration-compactness argument.
      PubDate: 2017-03-18
      DOI: 10.1007/s00526-017-1128-6
      Issue No: Vol. 56, No. 2 (2017)
  • Global gradient estimates for non-uniformly elliptic equations
    • Authors: Sun-Sig Byun; Jehan Oh
      Abstract: We consider a nonlinear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We establish the global Calderón–Zygmund type estimates for the distributional solution in the case that the boundary of the domain is of class \(C^{1,\beta }\) for some \(\beta >0\) .
      PubDate: 2017-03-18
      DOI: 10.1007/s00526-017-1148-2
      Issue No: Vol. 56, No. 2 (2017)
  • Semilinear elliptic equations with Hardy potential and subcritical source
    • Authors: Phuoc-Tai Nguyen
      Abstract: Let \(\Omega \) be a smooth bounded domain in \({\mathbb {R}}^N\) ( \(N>2\) ) and \(\delta (x):=\text {dist}\,(x,\partial \Omega )\) . Assume \(\mu \in {\mathbb {R}}_+, \nu \) is a nonnegative finite measure on \(\partial \Omega \) and \(g \in C(\Omega \times {\mathbb {R}}_+)\) . We study positive solutions of P $$\begin{aligned} -\Delta u - \frac{\mu }{\delta ^2} u = g(x,u) \text { in } \Omega , \qquad \text {tr}^*(u)=\nu . \end{aligned}$$ Here \(\text {tr}^*(u)\) denotes the normalized boundary trace of u which was recently introduced by Marcus and Nguyen (Ann Inst H Poincaré Anal Non Linéaire, 34, 69–88, 2017). We focus on the case \(0<\mu < C_H(\Omega )\) (the Hardy constant for \(\Omega \) ) and provide qualitative properties of positive solutions of (P). When \(g(x,u)=u^q\) with \(q>0\) , we prove that there is a critical value \(q^*\) (depending only on \(N, \mu \) ) for (P) in the sense that if \(q<q^*\) then (P) possesses a solution under a smallness assumption on \(\nu \) , but if \(q \ge q^*\) this problem admits no solution with isolated boundary singularity. Existence result is then extended to a more general setting where g is subcritical [see (1.28)]. We also investigate the case where g is linear or sublinear and give an existence result for (P).
      PubDate: 2017-03-17
      DOI: 10.1007/s00526-017-1144-6
      Issue No: Vol. 56, No. 2 (2017)
  • On minimizers for the isotropic–nematic interface problem
    • Authors: Jinhae Park; Wei Wang; Pingwen Zhang; Zhifei Zhang
      Abstract: In this paper, we investigate the structure and stability of the isotropic-nematic interface in 1-D. In the absence of the anisotropic energy, the uniaxial solution is the only global minimizer. In the presence of the anisotropic energy, the uniaxial solution with the homeotropic anchoring is stable for \(L_2<0\) and unstable for \(L_2>0\) . We also present many interesting open questions, some of which are related to De Giorgi conjecture.
      PubDate: 2017-03-17
      DOI: 10.1007/s00526-017-1131-y
      Issue No: Vol. 56, No. 2 (2017)
  • Global solutions of nonlinear Schrödinger equations
    • Authors: Martin Schechter
      Abstract: We study the nonlinear Schrödinger equation in \(\mathbb {R}^n\) without making any periodicity assumptions on the potential or on the nonlinear term. This prevents us from using concentration compactness methods. Our assumptions are such that the potential does not change the essential spectrum of the linear operator. This results in \([0, \infty )\) being the absolutely continuous part of the spectrum. If there are an infinite number of negative eigenvalues, they will converge to 0. In each case we obtain nontrivial solutions. We also obtain least energy solutions.
      PubDate: 2017-03-17
      DOI: 10.1007/s00526-017-1145-5
      Issue No: Vol. 56, No. 2 (2017)
  • Monotonicity of solutions for some nonlocal elliptic problems in
    • Authors: B. Barrios; L. Del Pezzo; J. García-Melián; A. Quaas
      Abstract: In this paper we consider classical solutions u of the semilinear fractional problem \((-\Delta )^s u = f(u)\) in \({\mathbb {R}}^N_+\) with \(u=0\) in \({\mathbb {R}}^N {\setminus } {\mathbb {R}}^N_+\) , where \((-\Delta )^s\) , \(0<s<1\) , stands for the fractional laplacian, \(N\ge 2\) , \({\mathbb {R}}^N_+=\{x=(x',x_N)\in {\mathbb {R}}^N{:}\ x_N>0\}\) is the half-space and \(f\in C^1\) is a given function. With no additional restriction on the function f, we show that bounded, nonnegative, nontrivial classical solutions are indeed positive in \({\mathbb {R}}^N_+\) and verify $$\begin{aligned} \frac{\partial u}{\partial x_N}>0 \quad \hbox {in } {\mathbb {R}}^N_+. \end{aligned}$$ This is in contrast with previously known results for the local case \(s=1\) , where nonnegative solutions which are not positive do exist and the monotonicity property above is not known to hold in general even for positive solutions when \(f(0)<0\) .
      PubDate: 2017-03-17
      DOI: 10.1007/s00526-017-1133-9
      Issue No: Vol. 56, No. 2 (2017)
  • On the effect of interactions beyond nearest neighbours on non-convex
           lattice systems
    • Authors: Roberto Alicandro; Giuliano Lazzaroni; Mariapia Palombaro
      Abstract: We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.
      PubDate: 2017-03-17
      DOI: 10.1007/s00526-017-1129-5
      Issue No: Vol. 56, No. 2 (2017)
  • Analytic aspects of the Tzitzéica equation: blow-up analysis and
           existence results
    • Authors: Aleks Jevnikar; Wen Yang
      Abstract: We are concerned with the following class of equations with exponential nonlinearities: $$\begin{aligned} \Delta u+h_1e^u-h_2e^{-2u}=0 \qquad \mathrm {in}~B_1\subset \mathbb {R}^2, \end{aligned}$$ which is related to the Tzitzéica equation. Here \(h_1, h_2\) are two smooth positive functions. The purpose of the paper is to initiate the analytical study of the above equation and to give a quite complete picture both for what concerns the blow-up phenomena and the existence issue. In the first part of the paper we provide a quantization of local blow-up masses associated to a blowing-up sequence of solutions. Next we exclude the presence of blow-up points on the boundary under the Dirichlet boundary conditions. In the second part of the paper we consider the Tzitzéica equation on compact surfaces: we start by proving a sharp Moser–Trudinger inequality related to this problem. Finally, we give a general existence result.
      PubDate: 2017-03-17
      DOI: 10.1007/s00526-017-1136-6
      Issue No: Vol. 56, No. 2 (2017)
  • Solitary waves for coupled nonlinear elliptic system with nonhomogeneous
    • Authors: Jun Wang
      Abstract: In present paper we consider a class of coupled elliptic system with nonhomogeneous nonlinearities. This type of system is related to the Raman amplification in a plasma. We make rigorous study and find the threshold conditions to guarantee the existence, nonexistence and multiplicity of nontrivial solutions for both two and three coupled system by using Morse theory, direct analysis methods and Krasnosel’skii–Rabinowitz global bifurcation theorem. Moreover, we study the asymptotical behavior of positive solutions, and prove some interesting phenomena for these solutions. Comparing to our previous works Wang and Shi (standing waves for weakly coupled Schrödinger equations with quadratic nonlinearities. Preprint, 2015) on the homogeneous case, we encounter some new challenges in proving the existence and multiplicity of nontrivial solutions. We overcome these difficult by combining the Mountain–Pass theorem in convex set and the Nehari constraint methods.
      PubDate: 2017-03-17
      DOI: 10.1007/s00526-017-1147-3
      Issue No: Vol. 56, No. 2 (2017)
  • Generalized Ginzburg–Landau equations in high dimensions
    • Authors: Yuxin Ge; Etienne Sandier; Peng Zhang
      Abstract: In this work, we study critical points of the generalized Ginzburg–Landau equations in dimensions \(n\ge 3\) which satisfy a suitable energy bound, but are not necessarily energy-minimizers. When the parameter in the equations tend to zero, such solutions are shown to converge to singular n-harmonic maps into spheres, and the convergence is strong away from a finite set consisting (1) of the infinite energy singularities of the limiting map, and (2) of points where bubbling off of finite energy n-harmonic maps could take place. The latter case is specific to dimensions \({>}2\) . We also exhibit a criticality condition satisfied by the limiting n-harmonic maps which constrains the location of the infinite energy singularities. Finally we construct an example of non-minimizing solutions to the generalized Ginzburg–Landau equations satisfying our assumptions.
      PubDate: 2017-03-16
      DOI: 10.1007/s00526-017-1134-8
      Issue No: Vol. 56, No. 2 (2017)
  • On the subRiemannian cut locus in a model of free two-step Carnot group
    • Authors: Annamaria Montanari; Daniele Morbidelli
      Abstract: We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two with three generators, giving a new, independent proof of a result by Myasnichenko (J Dyn Control Syst 8(4):573-597, 2002). We also calculate explicitly the cut time of any extremal path and the distance from the origin of all points of the cut locus. Furthermore, by using the Hamiltonian approach, we show that the cut time of strictly normal extremal paths is a smooth explicit function of the initial velocity covector. Finally, using our previous results, we show that at any cut point the distance has a corner-like singularity.
      PubDate: 2017-03-16
      DOI: 10.1007/s00526-017-1149-1
      Issue No: Vol. 56, No. 2 (2017)
  • Fractional Poincaré inequality with finite total Q -curvature
    • Authors: Yannick Sire; Yi Wang
      Abstract: In this paper, we prove several Poincaré inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the Q-curvature on noncompact complete manifolds.
      PubDate: 2017-03-15
      DOI: 10.1007/s00526-017-1146-4
      Issue No: Vol. 56, No. 2 (2017)
  • An eigenvalue problem for a fully nonlinear elliptic equation with
           gradient constraint
    • Authors: Ryan Hynd
      Abstract: We consider the problem of finding \(\lambda \in {\mathbb {R}}\) and a function \(u:{\mathbb {R}}^n\rightarrow {\mathbb {R}}\) that satisfy the PDE $$\begin{aligned} \max \left\{ \lambda + F(D^2u) -f(x),H(Du)\right\} =0, \quad x\in {\mathbb {R}}^n. \end{aligned}$$ Here F is elliptic, positively homogeneous and superadditive, f is convex and superlinear, and H is typically assumed to be convex. Examples of this type of PDE arise in the theory of singular ergodic control. We show that there is a unique \(\lambda ^*\) for which the above equation has a solution u with appropriate growth as \( x \rightarrow \infty \) . Moreover, associated to \(\lambda ^*\) is a convex solution \(u^*\) that has essentially bounded second derivatives, provided F is uniformly elliptic and H is uniformly convex. It is unknown whether or not \(u^*\) is unique up to an additive constant; however, we verify that this is the case when \(n=1\) or when F, f, H are “rotational.”
      PubDate: 2017-03-09
      DOI: 10.1007/s00526-017-1115-y
      Issue No: Vol. 56, No. 2 (2017)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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