Authors:Olivier GUIBÉ; Alip OROPEZA Pages: 889 - 910 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Olivier GUIBÉ, Alip OROPEZA In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type { - div ( B ( x , u ) ∇ u ) = f in Ω , u = 0 on Γ o B ( x , u ) ∇ u ⋅ n → + γ ( x ) h ( u ) = g on Γ 1 where f and g are the element of L 1 (Ω) and L 1 (Γ1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.

Authors:Alberto CABADA; Nikolay D. DIMITROV Pages: 911 - 926 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Alberto CABADA, Nikolay D. DIMITROV This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.

Authors:Qun LIU; Daqing JIANG; Ningzhong SHI; Tasawar HAYAT; Ahmed ALSAEDI Pages: 927 - 940 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Qun LIU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

Authors:Lingyan YANG; Xiaoguang LI; Yonghong WU; Louis CACCETTA Pages: 941 - 948 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Lingyan YANG, Xiaoguang LI, Yonghong WU, Louis CACCETTA For 2 < γ < min {4,n}, we consider the focusing Hartree equation (0.1) i u t + Δ u + ( x - γ * u 2 ) u = 0 , x ∈ R n . Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of − Δ Q + Q = ( x −γ * Q 2)Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0.1) if M [ u ] 1 - s c E [ u ] s c < M [ Q ] 1 - s c E [ Q ] s c ( s c = γ - 2 2 ) . In this paper, we consider the complementary case M [ u ] 1 - s c E [ u ] s c ≥ M [ Q ] 1 - s c E [ Q ] s c and obtain a criteria on blow-up and global existence for the Hartree equation (0.1).

Authors:Sun-Hye PARK Pages: 965 - 973 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Sun-Hye PARK In this paper, we consider a von Karman equation with infinite memory. For von Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for von Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.

Authors:Anyin XIA; Mingshu FAN; Shan LI Pages: 974 - 984 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Anyin XIA, Mingshu FAN, Shan LI This paper deals with the singularity and global regularity for a class of nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up occurs.

Authors:R. AGARWAL; S. HRISTOVA; P. KOPANOV; D. O'Regan Pages: 985 - 997 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): R. AGARWAL, S. HRISTOVA, P. KOPANOV, D. O'Regan Differential equations with impulses at random moments are set up and investigated. We study the case of Gamma distributed random moments of impulses. Several properties of solutions are studied based on properties of Gammma distributions. Some sufficient conditions for p-moment exponential stability of the solutions are given.

Authors:Xiaoxiao ZHENG; Yadong SHANG; Xiaoming PENG Pages: 998 - 1018 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Xiaoxiao ZHENG, Yadong SHANG, Xiaoming PENG This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations { i u t + u x x = u v + u 2 u , v t t - v x x = ( u 2 ) x x . First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].

Authors:Inomjon GANIEV; Farrukh MUKHAMEDOV Pages: 1019 - 1032 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Inomjon GANIEV, Farrukh MUKHAMEDOV In this paper we prove the existence of conditional expectations in the noncommutative L p (M,Φ)-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative L p (M,Φ)-spaces.

Authors:Jae-Myoung KIM Pages: 1033 - 1047 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Jae-Myoung KIM We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are Hölder continuous near boundary provided that the scaled mixed Lp,q x,t -norm of the velocity vector field with 3/p+2q ≤ 2, 2 < q < ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ɛ Lp,q x,t with 1 ≤ 3 p + 2 p ≤ 3 2 , 3 < p < ∞ , the Hausdorff dimension of its singular set is no greater than max {p,q} ( 3 p + 2 p - 1 ) .

Authors:Paweł SZAFRANIEC Pages: 1048 - 1060 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Paweł SZAFRANIEC In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.

Authors:Minjie JIANG; Wei YAN; Yimin ZHANG Pages: 1061 - 1082 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Minjie JIANG, Wei YAN, Yimin ZHANG This current paper is devoted to the Cauchy problem for higher order dispersive equation u t + ∂ x 2 n + 1 u = ∂ x ( u ∂ x n u ) + ∂ x n - 1 ( u x 2 ) , n ≥ 2 , n ∈ N + . By using Besov-type spaces, we prove that the associated problem is locally well-posed in H ( - n 2 + 3 4 , - 1 2 n ) ( R ) . The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H ( s , a ) ( R ) with s < - n 2 + 3 4 and all a ∈ R .

Authors:Wei DING; Yueping ZHU Pages: 1083 - 1104 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Wei DING, Yueping ZHU In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces F ˙ p α , q ( ω ; R n 1 × R n 2 ) based on the Frazier and Jawerth' method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that ( F ˙ p α , q ) * = CMO p - α , q ' for 0 < p ≤ 1.

Authors:Yunxia WEI; Yanping CHEN Pages: 1105 - 1114 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Yunxia WEI, Yanping CHEN This paper is concerned with obtaining theapproximate solution for Volterra-Hammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function ω(x)=1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L2 norm and L∞ norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method.

Authors:Feng CHENG; Wei-Xi LI; Chao-Jiang XU Pages: 1115 - 1132 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Feng CHENG, Wei-Xi LI, Chao-Jiang XU In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L 2-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

Authors:Tadeusz ANTCZAK Pages: 1133 - 1150 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Tadeusz ANTCZAK In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval-objective function are convex.

Authors:Chuanzhong LI Pages: 1151 - 1161 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Chuanzhong LI In this paper, we construct a new integrable equation called Möbius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the Möbius-Toda equation and a whole integrable Möbius-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the Möbius-Toda hierarchy are given and this leads to the existence of the tau function.

Authors:Qun HE; Fanqi ZENG; Daxiao ZENG Pages: 1162 - 1172 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Qun HE, Fanqi ZENG, Daxiao ZENG In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.

Authors:Guangjun SHEN; Xiuwei YIN; Litan YAN Pages: 1173 - 1176 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Guangjun SHEN, Xiuwei YIN, Litan YAN We give a correction of Theorem 2.2 of Shen, Yin and Yan (2016).

Authors:Boling GUO; Xiaoyu XI Pages: 573 - 583 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Boling GUO, Xiaoyu XI In this article, we are concerned with the global weak solutions to the 1D compressible viscous hydrodynamic equations with dispersion correction δ2 ρ((φ(ρ))xxφ′(ρ)x with φ(ρ)=ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial conditions. The diffusion term ɛuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [ 1 ] ( α = 1 2 ) to 0 < α ≤ 1. In addition, we perform the limit ɛ→ 0 with respect to 0 < α ≤ ½.

Authors:Dongyang SHI; Xin LIAO; Lele WANG Pages: 584 - 592 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Dongyang SHI, Xin LIAO, Lele WANG In this article, a nonconforming quadrilateral element (named modified quasi-Wilson element) is applied to solve the nonlinear schrödinger equation (NLSE). On the basis of a special character of this element, that is, its consistency error is of order O(h 3) for broken H 1-norm on arbitrary quadrilateral meshes, which is two order higher than its interpolation error, the optimal order error estimate and superclose property are obtained. Moreover, the global superconvergence result is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.

Authors:Ruirui YANG; Wei ZHANG; Xiangqing LIU Pages: 593 - 606 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Ruirui YANG, Wei ZHANG, Xiangqing LIU In this article, by using the method of invariant sets of descending flow, we obtain the existence of sign-changing solutions of p-biharmonic equations with Hardy potential in ℝN.

Authors:Miaokun WANG; Yuming CHU Pages: 607 - 622 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Miaokun WANG, Yuming CHU In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

Authors:Nguyen Van THIN Pages: 623 - 656 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Nguyen Van THIN In 1996, C. C. Yang and P. C. Hu [8] showed that: Let f be a transcendental meromorphic function on the complex plane, and a ≠ 0 be a complex number; then assume that n ≥ 2, n 1, …,n k are nonnegative integers such that n 1 + ⋯ + n k ≥ 1 ; thus f n ( f ′ ) n 1 ⋯ ( f ( k ) ) n k − a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥ 2. Namely, we prove that f n ( f ′ ) n 1 ⋯ ( f ( k ) ) n k − a ( z ) has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k ≥ 2, and a(z) ≡ 0 is a small function of f and n ≥ 2, n 1,…,n k are nonnegative integers satisfying n 1+…+ n k ≥ 1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by J. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y. Xu [10]. The main result of this article also leads to a counterexample to the converse of Bloch's principle.

Authors:Chunlei HE; Shoujun HUANG; Xiaomin XING Pages: 657 - 667 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Chunlei HE, Shoujun HUANG, Xiaomin XING This article concerns the self-similar solutions to the hyperbolic mean curvature flow (HMCF) for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.

Authors:Tianjiao XUE; Runling AN; Jinchuan HOU Pages: 668 - 678 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Tianjiao XUE, Runling AN, Jinchuan HOU Let A be a unital algebra and M be a unital A -bimodule. A linear map δ: A → M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ ( A ) ∘ B + A ∘ δ ( B ) = δ ( A ∘ B ) for any A , B ∈ A with A ○ B= P, here A ○ B = AB + BA is the usual Jordan product. In this article, we show that if A = A lg N is a Hilbert space nest algebra and M = B ( H ) , or A = M = B ( X ) , then, a linear map δ : A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B ( X ) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.

Authors:Dexing KONG; Qi LIU; Changming SONG Pages: 679 - 694 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Dexing KONG, Qi LIU, Changming SONG In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with “small” initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with “small” initial data.

Authors:Hyunjoo CHO Pages: 695 - 702 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Hyunjoo CHO It is known that any hypersurface in an almost complex space admits an almost contact manifold [11, 14]. In this article we show that a hyperplane in an almost contact manifold has an almost complex structure. Along with this result, we explain how to determine when an almost contact structure induces a contact structure, followed by examples of a manifold with a closed G 2-structure.

Authors:A. JAJARMI; M. HAJIPOUR Pages: 703 - 721 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): A. JAJARMI, M. HAJIPOUR This article presents an efficient parallel processing approach for solving the optimal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is first transformed into a sequence of lower-order decoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a matrix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedback suboptimal control, we apply a fast iterative algorithm with low computational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.

Authors:Taishun LIU; Qinghua XU Pages: 722 - 731 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Taishun LIU, Qinghua XU In this article, first, we establish the Fekete and Szegö inequality for an interesting subclass of biholomorphic functions in the open unit disk U . Second, we generalize this result to the bounded starlike circular domain in ℂn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

Authors:Xumin GU; Tian-Yi WANG Pages: 752 - 767 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Xumin GU, Tian-Yi WANG In this article, we study irrotational subsonic and subsonic-sonic flows with general conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences.

Authors:Xiaojing JIA; Ren'an JIA Pages: 768 - 785 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Xiaojing JIA, Ren'an JIA Feedback supply chain is a key structure in the supply chain system, and the development of feedback supply chain for biogas biomass energy is one of the important ways of the rural ecological civilization construction. Presently, the efficiency problem of biogas supply chain in rural China has been restricting the development of biogas biomass energy business. This article, on the basis of combination of regulation parameters, describes the dynamic changes in the system, using differential equations integrated with simulation to reveal the rules of regulation parameters to investigate the efficiency problem in the biogas supply chain. First of all, on the basis of the actual situation, the flow level and flow rate system structure model and simulation equation set are established for the biogas energy feedback supply chain from a scale livestock farm to peasant households; On the basis of the differentiability of the simulation equation a third order inhomogeneous differential equation with constant coefficients containing regulative parameters is established for the quantity of biogas stored in the feedback supply chain. A theorem and its corollaries are established for the operating efficiency of supply chain to reveal the change law of the quantity of biogas, the quantity of biogas consumed daily by peasant households and its standard-reaching rate as well as other variables.

Authors:Ning CUI; Zong-Xuan CHEN Pages: 786 - 798 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Ning CUI, Zong-Xuan CHEN In this article, we mainly devote to proving uniqueness results for entire functions sharing one small function CM with their shift and difference operator simultaneously. Let f(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f(z), f(z+c), and Δ c n f ( z ) share 0 CM, then f(z + c)≡ Af(z), where A(≠ 0) is a complex constant. Moreover, let a(z), b(z)(≢ 0) ∈ S(f) be periodic entire functions with period f ( z ) − a ( z ) , f ( z + c ) − a ( z ) , Δ c n f ( z ) − b ( z ) share 0 CM, then f(z + c) ≡ f(z).

Authors:Kanat S. TULENOV; Madi RAIKHAN Pages: 799 - 805 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Kanat S. TULENOV, Madi RAIKHAN In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.

Authors:Xing LI; Yan YONG Pages: 806 - 835 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Xing LI, Yan YONG In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L 2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.

Authors:Yanyan GUO Pages: 836 - 851 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Yanyan GUO In this article, we consider the fractional Laplacian equation { ( − Δ ) α / 2 u = K ( x ) f ( u ) , x ∈ ℝ + n , u ≡ 0 , x ∉ ℝ + n , where 0 < α < 2 , ℝ + n : = { x = ( x 1 , x 2 , ⋯ , x n ) x n > 0 } . When K is strictly decreasing with respect to x′ , the symmetry of positive solutions is proved, where x′=(x 1,x 2,ċċċ,x n−1) ∈ ℝ n − 1 . When K is strictly increasing with respect to x n or only depend on x n, the nonexistence of positive solutions is obtained.

Authors:Yu XIAO; Engui FAN; Jian XU Pages: 852 - 876 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Yu XIAO, Engui FAN, Jian XU Using the Fokas unified method, we consider the initial boundary value problem for the Fokas-Lenells equation on the finite interval. We present that the Neumann boundary data can be explicitly expressed by Dirichlet boundary conditions prescribed, and extend the idea of the linearizable boundary conditions for equations on the half line to Fokas-Lenells equation on the finite interval.

Authors:Nai-Sher YEH; Chung-Cheng KUO Pages: 877 - 888 Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Nai-Sher YEH, Chung-Cheng KUO We establish some left and right multiplicative perturbations of a local α-times integrated C-semigroup S(ċ) on a complex Banach space X with non-densely defined generator, which can be applied to obtain some additive perturbation results concerning S(ċ). Some growth conditions of the perturbations of S(ċ) are also established.

Authors:Martin G. GRIGORYAN; Stepan SARGSYAN Pages: 293 - 300 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Martin G. GRIGORYAN, Stepan SARGSYAN In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems: for any ε ∈ (0,1), there exists a measurable set E ⊂ [0,1) of measure bigger than 1 — ε such that for any function f ∈ L1 [0,1), it is possible to find a function g ∈ L1 [0,1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing.

Authors:Yansheng ZHONG; Chunyou SUN Pages: 301 - 315 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Yansheng ZHONG, Chunyou SUN A new approach is established to show that the semigroup {S(t)} t ≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in Lq (Ω) (2 ≤ q < ∞) with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space.

Authors:Jingjun GUO; Chujin LI Pages: 316 - 328 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Jingjun GUO, Chujin LI In this article, we study the existence of collision local time of two independent d-dimensional fractional Ornstein-Uhlenbeck processes X H 1 t and X˜ H 2 t , with different parameters H i ∈ (0,1),i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its' chaos expansion.

Authors:Alexander ALEKSANDROV; Elena ALEKSANDROVA; Alexey ZHABKO; Yangzhou CHEN Pages: 329 - 341 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, Yangzhou CHEN A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

Authors:Kazuhide NAKAJO Pages: 342 - 354 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Kazuhide NAKAJO Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {A n}nɛN be a family of monotone and Lipschitz continuos mappings of C into E*. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [10] for solving the variational inequality problem for {A n} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.

Authors:Lishuang PAN; An WANG Pages: 355 - 367 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Lishuang PAN, An WANG We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.

Authors:M. Syed ALI; J. YOGAMBIGAI; Jinde CAO Pages: 368 - 384 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): M. Syed ALI, J. YOGAMBIGAI, Jinde CAO In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin's formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Authors:Zaiyun ZHANG; Jianhua HUANG; Mingbao SUN Pages: 385 - 394 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Zaiyun ZHANG, Jianhua HUANG, Mingbao SUN In this article, we investigate the initial value problem(IVP) associated with the defocusing nonlinear wave equation on ℝ2 as follows: { ∂ t t u - Δ u = - u 3 , u ( 0 , x ) = u 0 ( x ) , ∂ t u ( 0 , x ) = u 1 ( x ) , where the initial data (u 0, u 1) ɛ H s(ℝ2) × Hs−1 (ℝ2). It is shown that the IVP is global well-posedness in Hs(ℝ2) × Hs−1(ℝ2) for any 1 > s > 2/5. The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].

Authors:Na BA; Jinjun DAI Pages: 405 - 424 Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Na BA, Jinjun DAI We study the bound states to nonlinear Schrödinger equations with electro-magnetic fields i h ∂ ψ ∂ t = ( h i ∇ - A ( x ) ) 2 ψ + V ( x ) ψ - K ( x ) p - 1 ψ = 0 , on ℝ + × ℝ N . Let G ( x ) = [ V ( x ) ] p + 1 p - 1 - N 2 [ K ( x ) ] - 2 p - 1 and suppose that G(x) has k local minimum points. For h > 0 small, we find multi-bump bound states ψh(x,t) = e −lEt/h Uh(χ) with Uh concentrating at the local minimum points of G(x) simultaneously as h → 0. The potentials V(x) and K(x) are allowed to be either compactly supported or unbounded at infinity.

Authors:Fei HOU Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Fei HOU This paper is a continue work of [4,5]. In the previous two papers, we studied the Cauchy problem of the multi-dimensional compressible Euler equations with time-depending damping term - μ ( 1 + t ) λ ρ u , where λ≥0 and μ > 0 are constants. We have showed that, for all λ≥0 and μ>0, the smooth solution to the Cauchy problem exists globally or blows up in finite time. In the present paper, instead of the Cauchy problem we consider the initial-boundary value problem in the half space ℝd + with space dimension d = 2,3. With the help of the special structure of the equations and the fluid vorticity, we overcome the difficulty arisen from the boundary effect. We prove that there exists a global smooth solution for 0 ≤ λ <1 when the initial data is close to its equilibrium state. In addition, exponential decay of the fluid vorticity will also be established.

Authors:Yue WANG Abstract: Publication date: May 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 3 Author(s): Yue WANG Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we obtain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.

Authors:Haibo Abstract: Publication date: March 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 2 Author(s): Haibo YU This article considers the global regularity to the initial-boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishing viscosities, we first establish the elliptic system for U x and b y, which are estimated by ∇ × ux and ∇ × by , respectively. Then, we establish the global estimates for ∇ × u and ∇ × b.