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26 December 2017, Volume 37 Issue 6 Previous Issue    Next Issue

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Removable Singularities of Weakly A-Harmonic Tensors Tong Yuxia, Zheng Shenzhou, Cheng Linna Acta mathematica scientia,Series A. 2017, 37 (6):  1001-1011.  Abstract ( 127 )   RICH HTML PDF (336KB) ( 78 )   Save This paper studies the A-harmonic equation d*A(x,du)=0, and acquires the removable singularities for weakly A-harmonic tensors by means of the Hodge decomposition and Caccioppoli estimation. References | Related Articles | Metrics

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Difference of Weighted Composition Operators Form F(p,q,s) Space to Hμ∞ Space Zhang Li, Chu Xiujiao Acta mathematica scientia,Series A. 2017, 37 (6):  1012-1028.  Abstract ( 85 )   RICH HTML PDF (347KB) ( 71 )   Save In this paper, according to the value of parameters of F(p,q,s), we study the boundedness and compactness of differences of two weighted composition operators from F(p,q,s) to Hμ∞ on the unit disk D. References | Related Articles | Metrics

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A Class of Generalized Invex Functions and Vector Variational Inequalities Li Ru, Yu Guolin, Liu Wei, Liu Sanyang Acta mathematica scientia,Series A. 2017, 37 (6):  1029-1039.  Abstract ( 105 )   RICH HTML PDF (318KB) ( 64 )   Save In this paper, a new kind of generalized invex functions, termed (α,ρ,η)-invex function, is introduced, and some examples are proposed to illustrate its existence. Under the assumption of (α,ρ,η)-invexity, it presents the close relationship between variational-like inequality and multi-objective programming. By using KKM theorem, the existence results are established for vector variational-like inequalities. References | Related Articles | Metrics

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The Theorems of Embedding Normed Cones into Normed Linear Spaces and the Hahn-Banach Extension Theorems Wang Jianyong Acta mathematica scientia,Series A. 2017, 37 (6):  1040-1052.  Abstract ( 125 )   RICH HTML PDF (396KB) ( 51 )   Save The problems of embedding normed cones into normed linear spaces and the problems of extending continuous linear functionals from normed cones to normed linear spaces are studied in this paper. In the first part, by geometric methods, the embedding theorems of normed cones into normed linear spaces are proved directly. In the second part, for a convex cone in a given normed linear space, via the SHARPNESS MODULUS of the convex cone, the equivalent relation of the extension norm derived from the conical norm with the original norm is studied. The Hahn-Banach positive extension theorems of continuous linear functionals from normed cones to normed linear spaces are obtained at last. References | Related Articles | Metrics

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The Two-Dimensional Riemann Problem for Isentropic Chaplygin Gas Chen Tingting, Qu Aifang, Wang Zhen Acta mathematica scientia,Series A. 2017, 37 (6):  1053-1061.  Abstract ( 159 )   RICH HTML PDF (572KB) ( 85 )   Save In this paper, we mainly study the two-dimensional Riemann problem of irrotational initially and isentropic Chaplygin gas with four piecewise constants. And we obtain the existence of the classical weak solution under the conditions on the large initial data. By using the generalized characteristic analysis method, we consider the situation that the initial discontinuities conduce to six elementary waves. Then we classify the structures constructed by these elementary waves. Moreover we get the necessary and sufficient conditions for the classical weak solutions of two representative wave structures for which we construct the piecewise smooth solutions. References | Related Articles | Metrics

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Oscillation of the Neutral Emden-Fowler Differential Equation Li Wenjuan, Tang Huo, Yu Yuanhong Acta mathematica scientia,Series A. 2017, 37 (6):  1062-1069.  Abstract ( 146 )   RICH HTML PDF (273KB) ( 68 )   Save In this work, we investigate the oscillation of the neutral Emden-Fowler differential equation (r(t)|z'(t)|α-1z'(t))'+p(t)|z'(t)|α-1z'(t)+q(t)|x(σ(t))|β-1x(σ(t))=0, where z(t)=x(t)+g(t)x(τ(t)). By using the generalized Riccati transformation and integral averaging technique, we establish some new oscillation criteria. These results extend and improve some existing results in the literature. References | Related Articles | Metrics

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Approximation of the Incompressible Navier-Stokes-Fourier System by the Artificial Compressibility Method Shao Guangming, Chai Xiaojuan Acta mathematica scientia,Series A. 2017, 37 (6):  1070-1084.  Abstract ( 119 )   RICH HTML PDF (344KB) ( 67 )   Save This paper investigates the approximation of the incompressible Navier-Stokes-Fourier system by the artificial compressibility method. We introduce a family of perturbed compressible Navier-Stokes-Fourier system, which approximate the incompressible Navier-Stokes-Fourier system as ∈➝0+. Then we prove the existence and the convergence of solutions for the perturbed compressible Navier-Stokes-Fourier system to the solutions of the incompressible Navier-Stokes-Fourier system. References | Related Articles | Metrics

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Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy Su Xiao, Wang Shubin Acta mathematica scientia,Series A. 2017, 37 (6):  1085-1093.  Abstract ( 106 )   RICH HTML PDF (306KB) ( 52 )   Save This paper investigates the initial-boundary value problem of the semilinear wave equation with strong damped terms. We provide the sufficient conditions of finite time blow-up of solutions with high initial energy under some reasonable restrictions on the initial data. In the case of the arbitrary positive initial energy, we also present the sufficient conditions of the existence of global solutions in the energy space. References | Related Articles | Metrics

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Stability and Uniqueness of Positive Solutions for a Food-Chain Model Li Haixia Acta mathematica scientia,Series A. 2017, 37 (6):  1094-1104.  Abstract ( 134 )   RICH HTML PDF (405KB) ( 70 )   Save A food-chain model with Leslie-Gower and Crowley-Martin functional response is investigated in this paper. The sufficient conditions for the existence of positive solutions are given by means of the fixed point index. Furthermore, use the regularity theory of elliptic equations, the nonexistence, stability and uniqueness of positive solutions are discussed. The results show that there exists a unique linearly stable positive solution under different conditions when the parameter c is large or bounded. Finally, some numerical simulations are presented to verify and complement the theoretical results. References | Related Articles | Metrics

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Biharmonic Systems Involving Critical Nonlinearities and Different Rellich-Type Potentials Kang Dongsheng, Xiong Ping Acta mathematica scientia,Series A. 2017, 37 (6):  1105-1118.  Abstract ( 101 )   RICH HTML PDF (361KB) ( 47 )   Save In this paper, a system of biharmonic equations is investigated, which involves multiple critical Sobolev nonlinearities and different Rellich-type terms. The minimizers of the related best Soblev constant are found under certain assumptions and the existence of solutions to the system is established by variational arguments. References | Related Articles | Metrics

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Existence and Multiplicity of Positive Solutions for the Superlinear Kirchhoff-Type Equations with Critical Sobolev Exponent Liao Jiafeng, Li Hongying Acta mathematica scientia,Series A. 2017, 37 (6):  1119-1124.  Abstract ( 113 )   RICH HTML PDF (323KB) ( 64 )   Save In this paper, we consider a class of superlinear Kirchhoff-type problems with Sobolev critical exponent. Using the variational method, we obtain the existence and multiplicity of positive solutions. Moreover, a global (PS) condition is obtained for this critical problem. References | Related Articles | Metrics

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A Remark on a Constrained Variational Problem Guo Helin, Wang Yunbo Acta mathematica scientia,Series A. 2017, 37 (6):  1125-1128.  Abstract ( 107 )   RICH HTML PDF (216KB) ( 85 )   Save In this paper, we mainly improve the existing result in Theorem 1.1 of paper[9] about the constrained variational problem, and we will give the explicit expression of the parameter c*. References | Related Articles | Metrics

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Existence of Traveling Waves in a Spatial Infectious Disease Model with Vaccination Guo Tingguang, Xu Zhiting Acta mathematica scientia,Series A. 2017, 37 (6):  1129-1147.  Abstract ( 119 )   RICH HTML PDF (469KB) ( 66 )   Save The current paper is devoted to investigate the existence of traveling waves in a spatial infectious disease model with vaccination. First, we propose a spatial infectious disease model with vaccination, and then study the well-posedness of it. Second, based on constructing a pair of the vector-value upper and lower solutions and the applications of Schauder's fixed point theorem, we show that the model admits nontrivial and positive traveling waves connecting the disease free equilibrium and the endemic equilibrium. Third, by Laplace transforms, we establish the non-existence of traveling waves for the model, in which the prior estimate of the exponential decay of the traveling wave solutions is obtained by the Stable Manifold Theorem. The approach in this paper provides an effective method to deal with more general high dimensional non-cooperative reaction-diffusion systems. References | Related Articles | Metrics

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Extinction and Distribution for an SIQS Epidemic Model with Quarantined-Adjusted Incidence Wei Fengying, Lin Qingteng Acta mathematica scientia,Series A. 2017, 37 (6):  1148-1161.  Abstract ( 121 )   RICH HTML PDF (508KB) ( 67 )   Save This paper discusses a stochastic SIQS epidemic model with the quarantined-adjusted incidence. We obtain that, the stochastic model admits a unique and global solution. Our research reveals that, when the intensities of the white noises are large enough, the solution of the stochastic model around the disease-free equilibrium will be extinct, and the density of the infective individuals will exponentially approach zero. When the intensities of the white noises are small enough, the positive solution of the stochastic model obeys a unique stationary distribution around the endemic equilibrium. Further, Under some sufficient conditions, the solution will asymptotically follow a three-dimensional normal distribution if the endemic equilibrium is stable, and the mean and the variance can be expressed by formulation. Moreover, the numerical simulations demonstrate the properties of the solution and give good explanations to our model. References | Related Articles | Metrics

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Analysis of a Stochastic Delayed Epidemic Model with a Non-Monotonic Incidence Rate Meng Xiaoying Acta mathematica scientia,Series A. 2017, 37 (6):  1162-1175.  Abstract ( 120 )   RICH HTML PDF (537KB) ( 64 )   Save Epidemic models are often subject to random perturbations. This article proposes a stochastic delayed epidemic model with a non-monotonic incidence rate. By the Lyapunov method and Itô's formula, the existence of a unique global positive solution of the model and the stability of the disease-free equilibrium of the model are proved. The asymptotic behavior around the endemic equilibrium of the associated definite model is obtained. Finally, numerical simulations are presented to illustrate the results. References | Related Articles | Metrics

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Consensus of High-Order Discrete-Time Multi-Agent Systems with Quantized Information Ge Yanrong, Qi Yaohui, Chen Yangzhou, Song Xuejun Acta mathematica scientia,Series A. 2017, 37 (6):  1176-1188.  Abstract ( 103 )   RICH HTML PDF (627KB) ( 62 )   Save We investigate the consensus problem of high-order discrete-time linear multi-agent systems (HDLMAS) under directed information topology with quantized link in this paper. Firstly, we propose a linear consensus protocol which consists of quantized information of the agent itself and its neighbors. Secondly, we solve the quantized consensus problem by proposing a linear transformation to translate it into a stability problem. Based on stability theory, we obtain necessary and sufficient criteria in terms of Schur stability of matrices, and present an analytical expression of the consensus function, which is depended on the communication topology, the system dynamic and the initial states of the whole system. Finally, we propose a design procedure of the gain matrices in the protocol by solving an algebraic Riccati inequality. References | Related Articles | Metrics