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25 February 2016, Volume 36 Issue 1 Previous Issue    Next Issue

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Exact Number of Solutions of a One-Dimensional Prescribed Mean Curvature Equation with General Nonlinearities Wei Dongyi Acta mathematica scientia,Series A. 2016, 36 (1):  1-13.  Abstract ( 529 )   RICH HTML PDF (366KB) ( 455 )   Save In this paper, an exact number of solutions is obtained for the one-dimensional prescribed mean curvature equation with general nonlinearities (including singular nonlinearities) by means of a detailed analysis of time-map method. References | Related Articles | Metrics

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Determinant Representation of Dark N-Soliton Solution for the Defocusing Modified Korteweg-de Vries Equation Yu Jing, Han Jingwei, Wang Lihong, He Jingsong Acta mathematica scientia,Series A. 2016, 36 (1):  14-26.  Abstract ( 211 )   RICH HTML PDF (751KB) ( 262 )   Save For coupled modified Korteweg-de Vries (mKdV) equation, we construct a new Darboux transformation (DT), whose Darboux matrix TN and transformed solutions q[N], r[N] are explicitly given in determinant form. When the reduction condition r=q* is imposed on the new DT and a periodic non-zero seed solution is considered, we obtain determinant representation of dark N-soliton solutions for the defocusing mKdV equation. Especially, we show that dark 1-soliton and dark 2-soliton are both smooth solutions, and furthermore, we show that dark N-soliton solutions are smooth at least on a certain domain. References | Related Articles | Metrics

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An Overdetermined Anisotropic Problem with Nonconstant Boundary Condition Ruan Qihua Acta mathematica scientia,Series A. 2016, 36 (1):  27-35.  Abstract ( 179 )   RICH HTML PDF (319KB) ( 85 )   Save Given an open bounded connected subset Ω of Rn with a norm H(ξ), we consider an overdetermined anisotropic problem of -div(H(∇u)∇ξH(∇u))=1 with the the following nonconstant boundary condition: H(∇u)2=cx·∇u and u=0 on the boundary ∂Ω. If this overdetermined anisotropic problem admits a solution in a suitable weak sense, then Ω is of the Wulff Shape. References | Related Articles | Metrics

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Asymptotic Behavior of the Solution for the Nonclassical Diffusion Equations with Fading Memory on the Whole Space R3 Ma Qiaozhen, Xu Ling, Zhang Yanjun Acta mathematica scientia,Series A. 2016, 36 (1):  36-48.  Abstract ( 187 )   RICH HTML PDF (384KB) ( 415 )   Save We prove the existence of global attractors for the nonclassical diffusion equations with fading memory ut-Δut-Δu-∫0∞k(s)Δu(t-s)ds+f(x, u)=g(x) defined on the entire space R3, where nonlinearity f(x, u) is critical. References | Related Articles | Metrics

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Existence and Multiplicity of Solutions to Schrödinger-Poisson System with Potentials Zhang Qi Acta mathematica scientia,Series A. 2016, 36 (1):  49-64.  Abstract ( 196 )   RICH HTML PDF (393KB) ( 166 )   Save In this paper, we discuss the existence and multiplicity solutions to the following Schrödinger-Poisson system with potentials  -Δu+λVu+φu=f(x,u),x∈R3 -Δφ=u2,x∈R3 where λ≥qslant1 is a parameter, the potential V∈C(R3, R+) and satisfies the more general assumptions. When f is 4-superlinear at infinity, we discuss the existence and multiplicity of solutions for λ≥1 large enough without the compactness of embedding of the work space. We also consider the existence of infinity many solutions with f satisfying the more general sublinear assumptions. References | Related Articles | Metrics

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Mountain Pass Solutions for Fractional Coupled Nonlinear Schrödinger Systems Wei Gongming, Li qing Acta mathematica scientia,Series A. 2016, 36 (1):  65-79.  Abstract ( 160 )   RICH HTML PDF (368KB) ( 202 )   Save In this paper, we study the existence of nontrivial solutions for fractional coupled nonlinear Schrödinger systems with Dirichlet boundary conditions. Our method is to use Mountain Pass Theorem in fractional order Sobolev spaces. The main points are to prove that the PS condition is satisfied and the mountain pass solution for the system is actually nontrivial. References | Related Articles | Metrics

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Pseudo Almost Periodic Solutions for a Model of Hematopoiesis with an Oscillating Circulation Loss Rate Jiang Ani Acta mathematica scientia,Series A. 2016, 36 (1):  80-89.  Abstract ( 148 )   RICH HTML PDF (812KB) ( 99 )   Save In this paper, a model of hematopoiesis with an oscillating circulation loss rate is investigated. By applying the exponential dichotomy theory, contraction mapping fixed point theorem and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of positive pseudo almost periodic solutions of the model. Some numerical simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies. References | Related Articles | Metrics

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Strichartz Estimates for the Wave Equation with the Full-Laplacian on the Quaternion Heisenberg Group Song Naiqi, Zhao Jiman Acta mathematica scientia,Series A. 2016, 36 (1):  90-116.  Abstract ( 177 )   RICH HTML PDF (475KB) ( 81 )   Save In this article, we prove dispersive and Strichartz estimates for the solution of the wave equation related to the full-Laplacian on the quaternion Heisenberg group, by means of homogeneous Besov space defined by a Littlewood-Paley decomposition related to the full-Laplacian. References | Related Articles | Metrics

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The Boundedness of the Commutator of Riesz Potential Associated with Schrödinger Operators Chen Dongxiang, Zhou Wenjuan, Fang Yuda Acta mathematica scientia,Series A. 2016, 36 (1):  117-129.  Abstract ( 178 )   RICH HTML PDF (292KB) ( 64 )   Save Let L=-Δ+V be the Schrödinger operator, where Δ is the Laplacian on Rd and V≠0 is a nonnegative function satisfying the reverse Hölder inequality. The authors obtain the boundedness of the commutator for Riesz potential [b, IαL] associated with L on the Campanato-type spaces ΛLβ, for b∈BMO. References | Related Articles | Metrics

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On Existence and Asymptotic Behavior of Solutions for Functional Integral Equation of Volterra-Stieltjes Type Xia Zhinan Acta mathematica scientia,Series A. 2016, 36 (1):  130-143.  Abstract ( 174 )   RICH HTML PDF (320KB) ( 200 )   Save The aim of this paper is to present existence and asymptotic behavior of solutions for the quadratic functional integral equation of Volterra-Stieltjes type on unbounded interval. The concept of measure of noncompactness and the Schauder fixed point principle are the main tools in carrying out our proof. Furthermore, some examples are given to show the efficiency and usefulness of the main findings. References | Related Articles | Metrics

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Some Sufficient Conditions for Starlikeness and Convexity Fu Xiulian Acta mathematica scientia,Series A. 2016, 36 (1):  144-149.  Abstract ( 162 )   RICH HTML PDF (199KB) ( 69 )   Save Using lemmas in [1-3], we obtain some sufficient conditions for subordinations of zf'(z)/f(z) and starlikeness and convexity of f(z) by studying f(z), which generalizes the related results in [1-4]. References | Related Articles | Metrics

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Transformation and Reduction Formulae for Bivariate Hypergeometric Series Liu Hongmei, Zhou Wenshu, Li Yang Acta mathematica scientia,Series A. 2016, 36 (1):  150-156.  Abstract ( 177 )   RICH HTML PDF (247KB) ( 96 )   Save Two quadratic transformations are applied to establish two general transformation formulae for double hypergeometric series. Further new reduction formulae for the bivariate hypergeometric series of types F1:0;μ1:1;λ and F2:0;μ2:1;λ are given. References | Related Articles | Metrics

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Tripled Coincidence and Tripled Fixed Point Theorems for Compatible Mappings Under Contractive Conditions in Partially Ordered Probabilistic Metric Spaces Luo Ting, Zhu Chuanxi Acta mathematica scientia,Series A. 2016, 36 (1):  157-167.  Abstract ( 193 )   RICH HTML PDF (310KB) ( 144 )   Save In this paper, we establish the notion of compatibility for a pair of mappings G:X×X×X→X and g:X→X in partially ordered probabilistic metric spaces. Under not necessary commutative conditions, some tripled coincidence and tripled common fixed point problems of compatible mappings satisfying a more general nonlinear contractive condition are studied. The obtained results generalize some coupled common fixed point theorems in the corresponding literatures. Finally, an example is given to illustrate our main results. References | Related Articles | Metrics

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Approximation of Multidimensional Parameter Fractional Brownian Sheet in Skorokhod Space Wang Zhi, Jing Huiting, Yan Litan Acta mathematica scientia,Series A. 2016, 36 (1):  168-175.  Abstract ( 168 )   RICH HTML PDF (297KB) ( 74 )   Save In this paper, we prove a convergence in law of a random walk constructed using a family of independent identically distributed random variables to the multidimensional parameter fractional Brownian sheet in the Skorokhod space. References | Related Articles | Metrics

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Optimal Dividend-Payout in a MAP Risk Model Chen Xu, Yang Xiangqun Acta mathematica scientia,Series A. 2016, 36 (1):  176-186.  Abstract ( 202 )   RICH HTML PDF (364KB) ( 219 )   Save In this paper, we model the surplus process of the insurance by the classical compound Poisson risk model modulated by an continuous-time Markov chain, which is the phase process of a Markovian Arrival Process(MAP). The surplus process can't be observed continuously. The observation and the possible dividend are restricted to a sequence of random discrete time points which are determined by the same MAP. The insurance has only observation opportunities at some of these random time points, and has both observation and paying dividend opportunities at the other random time points. The object of the insurance is to select the dividend strategy that maximizes the expected total discounted dividend payments until ruin. The purpose of this paper is to analyze the impact of the paying dividend opportunity and the economic state on the value functions and dividend strategies. We show that the optimal dividend pay-out policy is a band policy at dividend pay-out times. References | Related Articles | Metrics

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Taxation Problems in the Dual Model with Capital Injections Liu Xiao, Chen Zhenlong Acta mathematica scientia,Series A. 2016, 36 (1):  187-192.  Abstract ( 144 )   RICH HTML PDF (347KB) ( 105 )   Save This paper studies the taxation problems in the dual model with capital injections. Assume that the taxes are paid according to a loss-carry-forward system. Let the surplus attain 0 avoiding ruin by capital injections when the surplus becomes negative. The explicit expression for the expected discounted tax payments minus the expected discounted costs of capital injections is obtained under the assumption that the gains are exponentially distributed. References | Related Articles | Metrics