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25 April 2015, Volume 35 Issue 2 Previous Issue    Next Issue

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Two Non-Negative Solutions of a Quasilinear Elliptic Equation on RN Zhang Zhengjie, Zhang Ying Acta mathematica scientia,Series A. 2015, 35 (2):  225-233.  Abstract ( 183 )   RICH HTML PDF (302KB) ( 177 )   Save In the paper, we used variational method to study a quasilinear elliptic equation on RN. We get that there exist two non-negative solutions for our problem, one solution is a local minimum and the other is of mountain pass type. References | Related Articles | Metrics

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Coupled Semilinear Parabolic System with Nonlinear Nonlocal Boundary Condition Ling Zhengqiu, Qin Siqian Acta mathematica scientia,Series A. 2015, 35 (2):  234-244.  Abstract ( 177 )   RICH HTML PDF (365KB) ( 137 )   Save This paper considers a semilinear parabolic system uit =Δui+ci(x,t)ui+1pi for (x,t)∈ Ω × (0,∞) subject to weighted nonlocal Dirichlet boundary conditions ∫Ωψi(x,y,t)uili (y,t)dy and nonnegative initial data. Some criteria on this problem which determine whether the solutions blow up in a finite time or the solutions exist for all time are given. These results show that the weight functions ci(x,t), ψi(x,y,t) and the size of exponents pi, li play substantial roles in determining whether the solutions are global or blow-up. References | Related Articles | Metrics

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The Distribution of Values of the Infinite Order Random Dirichlet Series on the Right Half-Plane Wang Zhigang, Tian Fanji Acta mathematica scientia,Series A. 2015, 35 (2):  245-255.  Abstract ( 178 )   RICH HTML PDF (383KB) ( 154 )   Save The emphasis in this paper is mainly on the distribution of values of the infinite order random Dirichlet series on the right half-plane. Firstly, the theorem of the growth and the distribution of value of the Dirichlet series on the right half-plane are proved under some weak conditions of the coefficient. Secondly, the random Dirichlet series the norms of whose coefficients are pairwise NQD sequences are investigated and some better results similar to the case of independent random sequences are obtained. Under some conditions, the random series Xne-λns and the series σne-λns a.s. have the same abscissa of convergence, the order of growth, the type function on the right half-plane. References | Related Articles | Metrics

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Normal Families of Meromorphic Functions and Multiple Values Zhao Lijuan Acta mathematica scientia,Series A. 2015, 35 (2):  256-263.  Abstract ( 181 )   RICH HTML PDF (271KB) ( 158 )   Save In this paper, we discuss the normal families of meromorphic functions related to the exceptional functions, which generalize and improvement the related results due to Fang[2] in some extent. References | Related Articles | Metrics

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An Extension for Ramanujan's Circular Summation and Its Applications Luo Qiuming Acta mathematica scientia,Series A. 2015, 35 (2):  264-273.  Abstract ( 174 )   RICH HTML PDF (264KB) ( 292 )   Save In this paper, we generalized the Ramanujan's circular summation formula and give an elementary proof of them. Some applications are also considered. References | Related Articles | Metrics

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Uniqueness of Algebroid Functions Concerning Small Functions Liu Huifang, Sun Daochun Acta mathematica scientia,Series A. 2015, 35 (2):  274-281.  Abstract ( 252 )   RICH HTML PDF (306KB) ( 162 )   Save In this paper, we investigate the uniqueness problem of two v-valued algebroid functions sharing 4v+1 distinct small algebroid functions, and extend some uniqueness theorems of meromorphic functions dealing with small meromorphic functions to algebroid functions. References | Related Articles | Metrics

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Decay Rate of Solutions to An Inhomogenerous Semilinear Biharmonic Equation in Entire Space Yang Fen Acta mathematica scientia,Series A. 2015, 35 (2):  282-287.  Abstract ( 140 )   RICH HTML PDF (266KB) ( 116 )   Save In this paper, we consider the existence of the positive solutions for the inhomogeneous biharmonic equation -Δ2u +up +f(x)=0, x∈Rn (*) where Δ2 is the biharmonic operator, p>1, n≥5, and f0 is a given nonnegative function. Based on [16], the existence of solutions with the third decay rate at infinity are established under the assumptions on f. References | Related Articles | Metrics

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Blow-up of Solutions for a Semilinear Hyperbolic Equation with Variable Exponent and Positive Energy Wang Hua, He Yijun Acta mathematica scientia,Series A. 2015, 35 (2):  288-293.  Abstract ( 164 )   RICH HTML PDF (262KB) ( 148 )   Save In this short work, we consider a class of semilinear hyperbolic equations with variable exponent utt=Δ u+up(x) with homogeneous Dirichlet boundary conditions. Under some appropriate assumptions on the parameters, and with certain initial data, a blow-up result is established with positive energy. References | Related Articles | Metrics

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Attractors for the Nonclassical Diffusion Equations with Critical Nonlinearity on the Whole Space R3 Zhang Yanjun, Ma Qiaozhen Acta mathematica scientia,Series A. 2015, 35 (2):  294-305.  Abstract ( 185 )   RICH HTML PDF (356KB) ( 145 )   Save We prove the existence of global attractor in H1(R3) for the nonclassical diffusion equation with critical nonlinearity ut-Δut-Δu+f(x,u)=g(x). The results generalize and improve some results in [15]. References | Related Articles | Metrics

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Remark on Isoperimetric Inequalities in the Wullf Case Ma Lei, Zeng Chunna Acta mathematica scientia,Series A. 2015, 35 (2):  306-311.  Abstract ( 169 )   RICH HTML PDF (286KB) ( 170 )   Save In this paper we investigate some isoperimetric inequalities in the Wulff case. Via certain quantity of convex domains variation (monotonicity, invariance) in the Wulff case, we give a simplified proof of Wulff-Gage isoperimetric inequality and the Wulff-entropy inequality for curvature. Finally, we obtain a new inequality in the Wulff case. References | Related Articles | Metrics

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The Symmetry of Solutions to a Fully Nonlinear Elliptic Equations Zhao Jinhu, Liu Baiyu, Xu Er Acta mathematica scientia,Series A. 2015, 35 (2):  312-323.  Abstract ( 198 )   RICH HTML PDF (337KB) ( 130 )   Save In this paper, we obtain a symmetry and monotonicity result for solutions of a fully nonlinear elliptic system in bounded domain. Our method employs the moving plane method with Hopf's lemma at a corner. References | Related Articles | Metrics

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Topological Uniform Descent and the Perturbation of Weyl's Theorem Cui Miaomiao, Cao Xiaohong Acta mathematica scientia,Series A. 2015, 35 (2):  324-331.  Abstract ( 161 )   RICH HTML PDF (317KB) ( 96 )   Save An operator T is said to satisfy Browder's theorem if σ(T)\σw(T)⊆π00(T), where σ(T) and σw(T) denote the spectrum and the Weyl spectrum respectively, and π00(T)={λ∈isoσ(T);0N(T-λI)< ∞}. If σ(T)\σw(T)=π00(T), we say T satisfies Weyl's theorem. Using the characteristics of Topological uniform descent domain, the stability of Browder's theorem under compact perturbations is investigated, and those operators which have this stability are characterized. References | Related Articles | Metrics

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Local Estimation of the Diffusion Coefficient for Time-Inhomogeneous Diffusion Models Wang Jixia, Xiao Qingxian Acta mathematica scientia,Series A. 2015, 35 (2):  332-344.  Abstract ( 159 )   RICH HTML PDF (358KB) ( 126 )   Save Based on discretely observed sample of the time-inhomogeneous diffusion models, the local estimation of the diffusion coefficient is proposed by using local approximate method. Furthermore, we verify the strong consistency and asymptotic normality of the local estimation proposed. References | Related Articles | Metrics

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Statistical Inference for Semiparametric Varying Coefficient Partially Linear Model with Missing Data Chen Panpan, Feng Sanying, Xue Liugen Acta mathematica scientia,Series A. 2015, 35 (2):  345-358.  Abstract ( 206 )   RICH HTML PDF (467KB) ( 172 )   Save In this paper, we consider the statistical inference for semiparametric varying coefficient partially linear model with covariates missing at random. The profile least-squares estimators for the unknown parametric and coefficient functions are obtained by inverse probability weighted least-squares method. The asymptotic normality of the proposed estimators are proved under some appropriate conditions. In addition, we constructed an empirical log-likelihood ratio statistic for the unknown parametric components, and it is shown that the proposed statistic has the asymptotic chi-square distribution, and hence it can be used to construct the confidence regions of the parameter. Simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed procedure. References | Related Articles | Metrics

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Groups Whose Proper Quotients Are Periodic FC-Groups Zhang Zhirang, Li Xiang Acta mathematica scientia,Series A. 2015, 35 (2):  359-363.  Abstract ( 136 )   RICH HTML PDF (274KB) ( 115 )   Save A group is an FC-group if all its conjugacy classes are finite and a group is a periodic FC-group if it is an FC-group all of whose elements have finite order. A group G is said to be a just non-(periodic FC)-group if all its proper quotients are periodic FC-groups, but G itself is not. The purpose of this article is to give a satisfied description of the structure of just non-(periodic FC)-groups. References | Related Articles | Metrics

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Multiplicity Result for Homoclinic Solutions to A Class of Subquadratic Hamiltonian Systems Sun Zhaohong, Zhang Wei, He Tieshan, Gao Chuanxiang Acta mathematica scientia,Series A. 2015, 35 (2):  364-372.  Abstract ( 153 )   RICH HTML PDF (364KB) ( 131 )   Save In the present paper we consider the multiplicity of homoclinic solutions for the second order non-autonomous subquadratic Hamiltonian system. In this case, the lower bounded coefficient of the potential function about u near infinity was required to be a positive constant in the literature. However, if the coefficient is a positive function but not a constant, the situation is quite different. In this paper we solved this question. We extent the coefficient to a positive function of t which minimum may be zero. Hence the result in this work is a significant improvement of the results in recent literature. References | Related Articles | Metrics

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Fractional Super-Yang Hierarchy and Its Super-Hamiltonian Structure Xia Dong, Xia Tiecheng, Li Desheng Acta mathematica scientia,Series A. 2015, 35 (2):  373-380.  Abstract ( 157 )   RICH HTML PDF (277KB) ( 123 )   Save Base on a fractional supertrace identity presented by Wang and Xia and the generalized zero curvature equation associated with Lie superalgebras, the fractional super-Yang hierarchy and its fractional super Hamiltonian structure are obtained. This method can be used other fractional super hierarchies. References | Related Articles | Metrics

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Hopf Bifurcation Analysis and Oscillatory Patterns of A Diffusive Gierer-Meinhardt Model Wan Aying, Yi Fengqi, Zheng Lifei Acta mathematica scientia,Series A. 2015, 35 (2):  381-394.  Abstract ( 171 )   RICH HTML PDF (813KB) ( 145 )   Save In this paper, a kind of diffusive Gierer-Meindardt model is considered. We performed detailed Hopf bifurcation analysis to this reaction diffusion systems. We not only prove the existence of Hopf bifurcations, but also derived the conditions to determine the bifurcation direction and the stability of the bifurcating periodic solutions. These results suggest the complex oscillatory patterns of this famous model. Computer simulations are included to support our theoretical analysis. References | Related Articles | Metrics

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T-Stability of Picard's Iteration in Cone Metric Spaces Huang Huaping, Xu Shaoyuan, Xu Wangbin Acta mathematica scientia,Series A. 2015, 35 (2):  395-404.  Abstract ( 217 )   RICH HTML PDF (318KB) ( 182 )   Save In this paper we investigate the T-stability of fixed point Picard's iteration procedures for contractive mappings and expansive mappings, respectively. We illustrate our conclusions for some examples. Furthermore, we use our results to obtain the unique positive solution for an ordinary differential equation with boundary conditions. References | Related Articles | Metrics

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Well-Posedness for Fractional Neutral Impulsive Stochastic Integro-Differential Equations Diem Dang Huan, Gao Hongjun Acta mathematica scientia,Series A. 2015, 35 (2):  405-421.  Abstract ( 285 )   RICH HTML PDF (426KB) ( 162 )   Save This paper deals with the well-posedness of mild solutions for a class of fractional neutral impulsive stochastic integro-differential equations with infinite delay in Hilbert spaces. The results are obtained by using the Sadovskii fixed point theorem combined with theories of α-resolvent operators. An example is provided to illustrate the effectiveness of the proposed results. References | Related Articles | Metrics

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Convergence Theorems of Composite Implied Iterative Scheme for Mixed Type Asymptotically Nonexpansive Mappings Liu Yongquan, Guo Weiping Acta mathematica scientia,Series A. 2015, 35 (2):  422-440.  Abstract ( 194 )   RICH HTML PDF (348KB) ( 123 )   Save The purpose of this paper is to study the weak and strong convergence of a new composite implicit iteration scheme to a common fixed point for a finite family of asmptotically nonexpansive self-mappings and a finite family of asymptotically nonexpansive nonself-mappings in Banach spaces. The results showed in this paper extend and improve the corresponding results of several authors. References | Related Articles | Metrics

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Common Fixed Point Results for Mappings Satisfying Contractive Conditions of Integral Type on W-Spaces Piao Yongjie Acta mathematica scientia,Series A. 2015, 35 (2):  441-448.  Abstract ( 143 )   RICH HTML PDF (297KB) ( 156 )   Save Two real functional sets Φ and Ψ are introduced, mappings satisfying two deferent contractive conditions of integral type on W-spaces are considered, and then that mappings have a unique common fixed point, if they satisfy converse commuting property or have a commuting point, is proved. At the same time, some particular forms are given. The obtained results here generalize and improve many generalizations of Banach contraction principle. References | Related Articles | Metrics

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The Product of Differentiation and Multiplication Operator from the Mixed-norm to the Bloch-type Space YU Yan-Yan, LIU Yong-Min Acta mathematica scientia,Series A. 2015, 35 (2):  68-79.  Abstract ( 1335 )   RICH HTML PDF (328KB) ( 346 )   Save Let H(\rm {\Bbb D})$ be the space of analytic functions on the unit disk ${\rm {\Bbb D}}$ and $u \in H(\rm {\Bbb D})$.The boundedness and compactness of the  product $DM_u$ of differentiation operator and multiplication operator from the mixed norm to the Bloch-type space are investigated in this paper. References | Related Articles | Metrics