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26 December 2016, Volume 36 Issue 6 Previous Issue    Next Issue

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Set-Valued Maps with Graphs of Finite Area Tu Qiang, Chen Wenyi Acta mathematica scientia,Series A. 2016, 36 (6):  1017-1026.  Abstract ( 140 )   RICH HTML PDF (338KB) ( 166 )   Save In this paper, we give a characterization of functions of bounded variation by using set-valued maps and show that for any upper semi-continuous set-valued map F with closed, convex images and graph of finite area, there exists a measurable selection of F which is a function of bounded variation. Moreover, the rectifiable graphs of such maps can be approximated weakly in the sense of currents and in area by graphs of smooth maps. References | Related Articles | Metrics

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Surfaces in Products of Semi-Riemannian Space Forms with Parallel Mean Curvature Vector Qiu Wanghua, Hou Zhonghua Acta mathematica scientia,Series A. 2016, 36 (6):  1027-1039.  Abstract ( 143 )   RICH HTML PDF (366KB) ( 142 )   Save Batista introduced a special (1,1) tensor S on a CMC immersed surface Σ2 in M2(c)×R. Later on, Fetcu and Rosebberg extended (1,1) tensor S to PMC surface Σ2Mn-1(c)×R. In the present paper, the authors consider a more general tensor S on PMC immersed surface Σ2 in Lorentzian product spaces (Mn-1(c)×R, g-1) and Riemmannian product spaces (Mn-1(c)×R, g+1). The authors compute the Simons type equations of |S|2, and characterize CMC surfaces in (M2(c)×R, gε). For case ε=+1, we obtain several pinching constants greater than that given by Batista. References | Related Articles | Metrics

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Some Characterizations of Bloch-type Spaces Fu Xi, Lu Bowen Acta mathematica scientia,Series A. 2016, 36 (6):  1040-1047.  Abstract ( 156 )   RICH HTML PDF (278KB) ( 169 )   Save In this paper, we investigate some properties for Bloch-type spaces of harmonic mappings in the unit disc D and unit ball Bn of Cn. By using the pseudo-hyperbolic distance function in Bn, some derivative-free characterizations of harmonic Bloch-type spaces are obtained. This extends the corresponding known ones of holomorphic and harmonic mappings due to Chen et al. in[1-3]. References | Related Articles | Metrics

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The Hausdorff Dimnension of the Julia Set Concerning Phase Transitions Wang Youming Acta mathematica scientia,Series A. 2016, 36 (6):  1048-1056.  Abstract ( 159 )   RICH HTML PDF (373KB) ( 133 )   Save Considering the sets of the points corresponding to the phase transitions of the Potts model on the diamond hierarchical lattice for antiferromagnetic coupling, it is shown that these sets are the Julia sets of a family of rational mappings. In this paper, we prove that they may be buried points of J(Tλ(z)) for some λ∈R. Further, the asymptotic formula of the Hausdorff dimension of the Julia set is given as λ→∞, which gives a lower bound the Hausdorff dimension of the Julia set of J(Tλ(z)). Finally, other topological structures of Julia set are discussed completely. References | Related Articles | Metrics

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Estimations of Convexity Radius and the Norm of Pre-Schwarz Derivative for Close to Convex Harmonic Mappings Qi Yi, Shi Qingtian Acta mathematica scientia,Series A. 2016, 36 (6):  1057-1066.  Abstract ( 145 )   RICH HTML PDF (343KB) ( 249 )   Save In this paper, the following subclass of H P0(α)={f=h+g∈H:Re{h'(z)-α}>|g'(z)|, z∈D and g'(0)=0} is studied, where α∈[0,1) and H is the class of all normalized sense preserving harmonic mappings defined in the unit disk D. Estimations of the convexity and starlike radii of P0(α) are given, which improve the relative results in[8, 9]. A distortion theorem and a lower bound of |f(D)| for all f∈P0(α) are obtained. The upper bound of Pre-Schwarzian norms of functions in a subclass of SHU containing P0(α) is estimated and the quasiconformality is discussed also. References | Related Articles | Metrics

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Oscillation Criteria for Generalized Neutral Emden-Fowler Equations Zeng Yunhui, Luo Liping, Yu Yuanhong Acta mathematica scientia,Series A. 2016, 36 (6):  1067-1081.  Abstract ( 120 )   RICH HTML PDF (331KB) ( 164 )   Save Oscillation criteria are established for generalized neutral Emden-Fowler equations of the form (r(t)|y'(t)|α-1y'(t))'+f(t,x(σ(t)))=0, t≥t0, where α>0,y(t)=x(t)+p(t)x(τ(t)),-μ≤p(t)≤1,μ∈(0,1). Our results improve and extend some known results in the literature, recently. Some illustrating examples are also provided to show the importance of our results. References | Related Articles | Metrics

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Covering Properties for Rarefied Sets Associated with the Stationary Schrödinger Operator at Infinity in a Cone Long Pinhong, Han Huili, Deng Guantie Acta mathematica scientia,Series A. 2016, 36 (6):  1082-1091.  Abstract ( 126 )   RICH HTML PDF (359KB) ( 189 )   Save In the paper we obtain the value distribution of Green potential and Poisson integral with respect to any positive measure associated with the stationary Schrödinger operator at infinity in a cone, then put forward a covering property for a-rarefied sets. References | Related Articles | Metrics

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Multi-Symplectic Fourier Pseudospectral Method for a DGH Equation Wang Junjie, Wang Liantang Acta mathematica scientia,Series A. 2016, 36 (6):  1092-1102.  Abstract ( 138 )   RICH HTML PDF (1011KB) ( 151 )   Save The DGH equation, an important nonlinear wave equation, has broad application prospect. With the canonical momenta, the multi-symplectic formulations for the DGH equation are presented. The multi-symplectic Fourier pseudospectral method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the DGH equation. The numerical experiments for DGH equation are given, showing that the multi-symplectic Fourier pseudospectral method is an efficient algorithm with excellent long-time numerical behaviors. References | Related Articles | Metrics

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Schrödinger Equation with Asymptotically Linear Nonlinearity and Spectrum Point Zero Qin Dongdong, Li Yunyang, Tang Xianhua Acta mathematica scientia,Series A. 2016, 36 (6):  1103-1116.  Abstract ( 142 )   RICH HTML PDF (412KB) ( 137 )   Save This paper is concerned with the following Schrödinger equation -△u+V(x)u=f(x, u), for x∈RN, u(x)→0, as |x|→∞, where V and f are both periodic in x and 0 is a boundary point of the spectrum σ(-△+V). Inspired by recent work of Tang[35], we consider further the case that f(x,u) is asymptotically linear as |u|→∞, and obtain the existence of ground state solutions using the non-Nehari manifold method which is more direct and simpler than the generalized manifold method. References | Related Articles | Metrics

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A Sharp Threshold of Blow-Up of a Class of Schrödinger-Hartree Equations Yang Lingyan, Li Xiaoguang, Chen Ying Acta mathematica scientia,Series A. 2016, 36 (6):  1117-1123.  Abstract ( 171 )   RICH HTML PDF (286KB) ( 158 )   Save In this paper, the Schrödinger-Hartree equation i∂tψ+△ψ=-(|x|-1*|ψ|α)|ψ|α-2}ψ, t>0,x∈R3,α≥2 (P) is considered in R3. We establish invariant evolution flows of the equation by Gagliardo-Nirenberg inequality, mass conservation and energy conservation of the equation (P). When (7)/(3)≤α < 5, a sharp threshold of global existence and blow-up of the Cauthy problem is derived. References | Related Articles | Metrics

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Initial Boundary Value Problem for a Class Wave Equation with Logarithmic Source Term Zhang Hongwei, Liu Gongwei, Hu Qingying Acta mathematica scientia,Series A. 2016, 36 (6):  1124-1136.  Abstract ( 202 )   RICH HTML PDF (387KB) ( 227 )   Save In this paper we consider the initial boundary value problem for a class wave equation with logarithmic source term. By using Galerkin method combining with the logarithmic Sobolev inequality and logarithmic Gronwall inequality, we obtain the existence of global solution for all initial data. By introducing potential well theory, we give the sufficient condition of the blow-up property in infinity time (i.e. exponential growth) of the solution. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for the wave equation with logarithmic source term and linear damping term. References | Related Articles | Metrics

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Multiple Solutions for Semilinear Elliptic Equations with Critical Exponents and Hardy Potential Yuan Haihua, Zhang Zhengjie, Xu Guojin Acta mathematica scientia,Series A. 2016, 36 (6):  1137-1144.  Abstract ( 129 )   RICH HTML PDF (298KB) ( 156 )   Save In this paper, we consider the following problem -△u+(u)/(|x|2)=|u|2*-2u+g(x),x∈RN, u(x)→0(|x|→∞),u∈D1,2(RN) where g(x)≥0,g(x)≠0, 且g(x)∈L(2N)/(N+2)(RN). We can prove that there exists a constant C, which is small enough,such that ‖g‖L(2N)/(N+2)(RN)≤C, then there are at least two solutions for the above problem. References | Related Articles | Metrics

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Fast Heteroclinic Solutions for a Difference Equation Related to Fisher-Kolmogorov's Equation Xu Jia, Wang Yanxia, Dai Guowei Acta mathematica scientia,Series A. 2016, 36 (6):  1145-1156.  Abstract ( 122 )   RICH HTML PDF (318KB) ( 126 )   Save In this paper, we prove the existence of fast heteroclinic solutions for a second-order difference equation related to traveling wave solutions of Fisher-Kolmogorov's equation. By means of variational approach, the fast heteroclinic solutions are obtained as minimizers of an energy functional on a weighted Hilbert space. References | Related Articles | Metrics

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Existence and Uniqueness of Solutions for Nonlocal Cauchy Problem for Fractional Evolution Equations Deng Jiqin, Deng Ziming Acta mathematica scientia,Series A. 2016, 36 (6):  1157-1164.  Abstract ( 220 )   RICH HTML PDF (295KB) ( 169 )   Save In this paper, by using the fixed point theorem and a new method, we study the existence and uniqueness of solutions for nonlocal Cauchy problem for fractional evolution equations with Caputo fractional derivative, and obtain two new results. Finally, to illustrate the theoretical results obtained, we give an example. References | Related Articles | Metrics

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Weighted Estimates on the Neumann Problem for L2 for Schrödinger Equations in Lipschitz Domains Huang Wenli, Tao Xiangxing Acta mathematica scientia,Series A. 2016, 36 (6):  1165-1185.  Abstract ( 135 )   RICH HTML PDF (437KB) ( 145 )   Save In this paper, we consider the weighted estimates in the weighted space Hp(∂Ω,ωαdσ) or Lp(∂Ω,ωαdσ)(1-ε < p≤2) for Schrödinger equation -Δu+Vu=0 on Lipschitz domains. Let Ω be a bounded Lipschitz domain with connected boundary in Rn, n≥3. Let ωα(Q)=|Q-Q0|α, where Q0 is a fixed point on ∂Ω. For Schrödinger equation -Δu+Vu=0 in Ω, with singular non-negative potentials V belonging to the reverse Hölder class Bn, we study the Neumann problem with boundary date lies in the weighted space Hp(∂Ω,ωαdσ) or Lp(∂Ω,ωαdσ), where dσ denotes the surface measure on ∂Ω. We show that for certain ranges of α, there is a unique solution u, such that the non-tangential maximal function of ▽u is in Hp(∂Ω,ωαdσ) or Lp(∂Ω,ωαdσ). Moreover, the uniform estimates are founded. References | Related Articles | Metrics

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Blow up and Lifespan Estimates for Initial Boundary Value Problem of Semilinear Schrödinger Equations on Half-Life Geng Jinbo, Yang Zhenzhen, Lai Ning-An Acta mathematica scientia,Series A. 2016, 36 (6):  1186-1195.  Abstract ( 164 )   RICH HTML PDF (310KB) ( 128 )   Save In this paper, we consider the initial boundary value problem of semilinear Schrödinger equation on half-line. Blow up result will be established, assuming the power of the nonlinear term satisfying 1 < p≤2. Furthermore, we obtain the upper bound of the lifespan in the case 1 < p < 2. The proof is based on a contradiction argument, by constructing a special test function. References | Related Articles | Metrics

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Long Time Behavior of Boussinesq Type Equation with Damping Term Geng Fan, Li Ruizhai, Ge Xiangyu Acta mathematica scientia,Series A. 2016, 36 (6):  1196-1210.  Abstract ( 134 )   RICH HTML PDF (414KB) ( 148 )   Save In this paper, we study the long time behavior of the solution of the initial boundary value problem of Boussinesq type equation with damping term:utt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is that the existence of global attractor of the infinite dimensional dynamical system and the existence of the global attractor and the Hausdorff dimension of the attractor in the phase space E=V2×H are proved by the method of semi group decomposition, The abstract ondition of nonlinear term g(u) is verified and given a concrete example. References | Related Articles | Metrics

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Potential Well and Application to Non-Newtonian Filtration Equations at Critical Initial Energy Level Liu Yang Acta mathematica scientia,Series A. 2016, 36 (6):  1211-1220.  Abstract ( 178 )   RICH HTML PDF (343KB) ( 137 )   Save This paper is concerned with the initial boundary value problem of non-Newtonian filtration equations at critical initial energy level. We first construct a new potential well and its outside set, and prove their invariance. Furthermore, the global existence and finite time blow-up of solutions are obtained. References | Related Articles | Metrics