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25 August 2015, Volume 35 Issue 4 Previous Issue    Next Issue

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Exponential Attractors for Reaction-Diffusion Equations in H2(Ω) and L2P-2(Ω) Wang Gang, Tang Yanbin Acta mathematica scientia,Series A. 2015, 35 (4):  641-650.  Abstract ( 132 )   RICH HTML PDF (344KB) ( 218 )   Save A class of reaction-diffusion equations with arbitrary polynomial growth nonlinearity f and nonhomogeneous term g are concerned in this paper. We first construct exponential attractors in H2(Ω) for the underlying semigroup when Ω is a bounded open set in R3. We obtain this result by proving the Lipschitz continuity between some positively invariant absorbing set in L2(Ω) and some positively invariant absorbing set in H2(Ω). Then, we obtain exponential attractors in L2P-2(Ω) for any g∈ L2(Ω) by using a new approaching technique. This improves the result in previous references. References | Related Articles | Metrics

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Ground State Solutions for A Periodic Schrödinger Equation with Critical Sobolev Exponent Xu Na, Ma Shiwang Acta mathematica scientia,Series A. 2015, 35 (4):  651-655.  Abstract ( 155 )   RICH HTML PDF (261KB) ( 178 )   Save In this note, we obtain the existence of ground state solutions for the following periodic Schrödinger equation -Δ u +V(x)u=K(x)|u|2*-2 u+g(x,u), u∈ H1(RN), where N≥ 4 and 2*=(2N)/(N-2) is the critical Sobolev exponent. Our result is a complement to some recent works concerning the existence of ground state solutions of the above equation. References | Related Articles | Metrics

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der Continuity of the Gradients of Weak Solutions to A-Harmonic Equation with Variable Exponents Tong Yuxia, Zheng Shenzhou, Yu Haiyan Acta mathematica scientia,Series A. 2015, 35 (4):  656-667.  Abstract ( 139 )   RICH HTML PDF (307KB) ( 168 )   Save This paper mainly concerns A-harmonic equation div A(x,▽u)=B(x,▽u) with variable exponents. We give local Hölder continuity of the gradients of weak solutions. References | Related Articles | Metrics

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Existence and Multiplicity Results for Schrödinger-Poisson System with Superlinear or Sublinear Terms Ye Yiwei, Tang Chunlei Acta mathematica scientia,Series A. 2015, 35 (4):  668-682.  Abstract ( 208 )   RICH HTML PDF (391KB) ( 185 )   Save In this paper, we study the existence and multiplicity of solutions for the Schrödinger-Poisson system  where V∈ C(R3, R) and K∈ L2∪ L∞ with K≥ 0. Without assuming the Ambrosetti-Rabinowitz type superquadratic condition and the monotonicity of the function t→(f(x,t))/(t3), we prove the existence of infinitely many high-energy solutions by using symmetric mountain pass theorem. We also consider the case where f is sublinear and establish the existence and multiplicity. References | Related Articles | Metrics

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New Subclasses of Spirallike Mappings Wang Chaojun, Cui Yanyan, Liu Hao, Zhu Sifeng Acta mathematica scientia,Series A. 2015, 35 (4):  683-694.  Abstract ( 189 )   RICH HTML PDF (361KB) ( 126 )   Save In this paper, we introduce some new subclasses of spirallike functions, namely elliptical starlike functions of order ρ, elliptical and spirallike functions of type β and order ρ. We extend the new definitions and obtain that the generalized Roper-Suffridge operators preserve the properties of the mappings defined in this paper on different domains in different spaces, thus many elliptical and spirallike mappings of type β and order ρ can be constructed in several complex variables. The conclusions enrich the research of subclasses of spirallike mappings and generalized Roper-Suffridge operators. References | Related Articles | Metrics

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Strong Convergence Based on Generalized Wiener-Hopf Equation Techniques for Solving Generalized Equilibrium Problems Wang Yuehu, Zhang Congjun Acta mathematica scientia,Series A. 2015, 35 (4):  695-709.  Abstract ( 144 )   RICH HTML PDF (373KB) ( 107 )   Save In this paper, we use generalized Wiener-Hopf equation techniques to construct an iterative scheme for generalized mixed equilibrium problems, an infinite family of non-expansive mappings and variational inequality problems. Furthermore, two strong convergence theorems are also established based on different monotonicity in Hilbert spaces. Finally, we utilize our results to study several optimization problems. The methods and results presented in this paper are different from the ones announced by many others and they extend the results of Shi and Noor. References | Related Articles | Metrics

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On Reverse Young and Heinz Inequalities for τ-Measurable Operators Shao Jingjing, Han Yazhou Acta mathematica scientia,Series A. 2015, 35 (4):  710-718.  Abstract ( 170 )   RICH HTML PDF (282KB) ( 147 )   Save Besides the singular value inequalities for the arithmetic, geometric and Heinz means of τ-measurable operators, we mainly establish reverse Young and Heinz inequalities for τ-measurable operators and for the norm ||·||2. References | Related Articles | Metrics

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Existence of Stationary Solutions to Euler-Poisson Equations with 1< γ< 6/5 Xiang Jianlin, Fang Xi, Deng Yanfang Acta mathematica scientia,Series A. 2015, 35 (4):  719-728.  Abstract ( 165 )   RICH HTML PDF (339KB) ( 104 )   Save The compressible Euler-Poisson system, addressed to describe the time evolution of self-induced gravitational gaseous stars, consists of the Euler equations for the conservation of mass, momentum and energy, and Poisson equation induced by the potential function of the self-gravitational force. We consider stationary solutions of the Euler-Poisson equations, i.e. the solutions independent of time t, for some velocity fields and smooth entropy functions that solve the conservation of mass and energy. When 1< γ< 6/5 and the entropy function satisfies some smooth property, we introduce a nonlinear transformation to turn the Euler-Poisson system into a semilinear elliptic equation, and then obtain the existence of the stationary solutions by a similar Pohozaev's identity proved in section 2. References | Related Articles | Metrics

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Complete Convergence for Sung's Type Weighted Sums Under NOD Setup Li Wei Acta mathematica scientia,Series A. 2015, 35 (4):  729-737.  Abstract ( 132 )   RICH HTML PDF (285KB) ( 170 )   Save The complete convergence for the weighted sums of identically distributed ρ*-mixing random variables in Sung is improved and extended under the NOD setup. The main tool in Sung is the maximum Rosenthal's type moemnt inequality, but it is unknown whether the kind of moment inequality holds or not for NOD, so our method is different from Sung's. References | Related Articles | Metrics

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Blow Up and Asymptotic Behavior in the Beam Equation Lei Qian, Li Ning, Yang Han Acta mathematica scientia,Series A. 2015, 35 (4):  738-747.  Abstract ( 147 )   RICH HTML PDF (340KB) ( 183 )   Save The initial-boundary value problem of the four order nonlinear wave equation (known as beam equation) is considered in this paper. Under the condition that the initial energy E0 is equal to the depth of potential well d, by constructing invariant sets, we obtain the sufficient conditions of the global existence and blow up of solutions for the nonlinear wave equation. Furthermore, the asymptotic properties of the global solutions have also been discussed. References | Related Articles | Metrics

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Weighted Composition Operators from α-Zygmund Spaces into β-Bloch Spaces Lu Heng, Zhang Taizhong Acta mathematica scientia,Series A. 2015, 35 (4):  748-755.  Abstract ( 188 )   RICH HTML PDF (270KB) ( 240 )   Save In this paper, we prove sufficient and necessary conditions for weighted composition operators from α-Zygmund spaces into β-Bloch spaces in the unit disk to be bounded and compact. References | Related Articles | Metrics

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large Convergence for Moving Average Processes Under END Set-up Qiu Dehua, Chen Pingyan Acta mathematica scientia,Series A. 2015, 35 (4):  756-768.  Abstract ( 150 )   RICH HTML PDF (349KB) ( 250 )   Save Let {Yn,-∞< n< +∞} be a doubly infinite sequence of non-identically distributed extended negatively dependent (END) random variables, {an,-∞< n< +∞} an absolutely summable sequence of real numbers. Utilizing the Rademacher-Menshov's inequality of END random variables, the complete convergence and complete moment convergence of the maximal partial sums of moving average processes Xn=ai Yi+n,n≥ are obtained, the corresponding results in series of previous papers are enriched and extended. References | Related Articles | Metrics

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The Chaos Behavior and Simulation of Three Model Systems of Couette-Taylor Flow Wang Heyuan Acta mathematica scientia,Series A. 2015, 35 (4):  769-779.  Abstract ( 186 )   RICH HTML PDF (623KB) ( 118 )   Save The dynamical behavior of a three-mode system of Couette-Taylor problem are studied, which is similar to the Lorenz equation. Condition of the stationary solutions, the existence of its attractor and the estimation of Hausdorff dimension are presented. The whole process, which shows bifurcation and chaos behavior with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, chaos behavior of the system are revealed. References | Related Articles | Metrics

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Two-Dimensional Differential Model and Numerical Method of Undersea Cables During Installation Han Huan, Li Xing, Liu Jun, Ni Chengzhou Acta mathematica scientia,Series A. 2015, 35 (4):  780-793.  Abstract ( 162 )   RICH HTML PDF (862KB) ( 155 )   Save In this paper, we establish a differential model to describe the installation process of undersea cable. At the same time, we put forward a numerical method to solve the mathematical model approximately and prove the existence of solution of the mathematical model in a special case. In practice, we can use the results in this paper to design the proper route of the messenger spacecraft to guarantee that the cable drop to the design position References | Related Articles | Metrics

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The Neumann Boundary Value Problems of Two Dimensional Monge-Ampère Equations Xiang Ni, Shi Juhua, Wang Yu'e Acta mathematica scientia,Series A. 2015, 35 (4):  794-802.  Abstract ( 193 )   RICH HTML PDF (309KB) ( 202 )   Save In this paper, we prove the second order derivatives estimates of Monge-Ampère type equations with Neumann boundary condition, using the method of auxiliary function which reduce the global estimates to the boundary. Then, we obtain the existence and regularity of the classical solutions for the equations. References | Related Articles | Metrics

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Oscillation for Emden-Fowler Delay Differential Equations of Neutral Type Zeng Yunhui, Luo liping, Yu Yuanhong Acta mathematica scientia,Series A. 2015, 35 (4):  803-814.  Abstract ( 189 )   RICH HTML PDF (332KB) ( 200 )   Save In this paper we establish some new oscillation criteria for the generalized Emden-Fowler delay differential equations of neutral type of the form (r(t)|z'(t)|α-1z'(t))'+q(t)|x(σ(t))|β-1x(σ(t))=0, where z(t)=x(t)+p(t)x(τ(t)),α>0,β>0. The results obtained improve and extend some known results in the literature, recently. References | Related Articles | Metrics

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Generalized Composition Operators from Zygmund Spaces and F(p,q,s) Spaces to Bμ Spaces Tan Chunyu, Wang Maofa Acta mathematica scientia,Series A. 2015, 35 (4):  815-823.  Abstract ( 127 )   RICH HTML PDF (294KB) ( 267 )   Save In this paper, we study generalized composition operators from Zygmund spaces and F(p,q,s) spaces to Bμ spaces and obtain some criterions of the boundedness and compactness, respectively. We also consider the generalized composition operators on the corresponding little spaces References | Related Articles | Metrics

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A Smoothing Inexact Newton Method for Symmetric Cone Complementarity Problems Zhang Yunsheng, Gao Leifu Acta mathematica scientia,Series A. 2015, 35 (4):  824-832.  Abstract ( 132 )   RICH HTML PDF (345KB) ( 200 )   Save Based on a smoothing function, an inexact smoothing Newton algorithm for large-scale symmetric cone complementarity problems is proposed. The algorithm is proved to be globally as well as locally quadratic convergence under proper conditions. Numerical experiments demonstrate that the algorithm is effective and feasible for large-scale problems. References | Related Articles | Metrics