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2019年, 第39卷, 第2期　刊出日期：2019-04-25 上一期   

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RIGIDITY THEOREMS OF COMPLETE KÄHLER-EINSTEIN MANIFOLDS AND COMPLEX SPACE FORMS 种田, 东瑜昕, 林和子, 任益斌 数学物理学报(英文版). 2019 (2):  339-356.  DOI: 10.1007/s10473-019-0201-y 摘要 ( 71 )   RICH HTML PDF   收藏 We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete Kähler manifolds. We derive some elliptic differential inequalities from Weitzenbock formulas for the traceless Ricci tensor of Kähler manifolds with constant scalar curvature and the Bochner tensor of Kähler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several Lp and L∞ pinching results are established to characterize Kähler-Einstein manifolds among Kähler manifolds with constant scalar curvature and complex space forms among Kähler-Einstein manifolds. Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact Kähler manifolds and noncompact Kähler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge, these kinds of results have not been reported. 参考文献 | 相关文章 | 计量指标

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LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS Phuong LE, Vu HO 数学物理学报(英文版). 2019 (2):  357-368.  DOI: 10.1007/s10473-019-0202-x 摘要 ( 62 )   RICH HTML PDF   收藏 This paper is devoted to the quasilinear equation where p ≥ 2, Ω is a (bounded or unbounded) domain of RN, w1, w2 are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω, w1, w2 and f, which extends and unifies several results on this topic. 参考文献 | 相关文章 | 计量指标

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APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES Iz-iddine EL-FASSI, Hamid KHODAEI, Themistocles M. RASSIAS 数学物理学报(英文版). 2019 (2):  369-381.  DOI: 10.1007/s10473-019-0203-9 摘要 ( 56 )   RICH HTML PDF   收藏 In this paper, using the Brzd?k’s fixed point theorem [9, Theorem 1] in non-Archimedean (2, β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation where p ∈ {1, …, 5}, a1, …, ak are fixed nonzero reals when p ∈ {1, 3, 5} and are fixed positive reals when p ∈ {2, 4}. 参考文献 | 相关文章 | 计量指标

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THE CHARACTERIZATION OF EFFICIENCY AND SADDLE POINT CRITERIA FOR MULTIOBJECTIVE OPTIMIZATION PROBLEM WITH VANISHING CONSTRAINTS Anurag JAYSWAL, Vivek SINGH 数学物理学报(英文版). 2019 (2):  382-394.  DOI: 10.1007/s10473-019-0204-8 摘要 ( 41 )   RICH HTML PDF   收藏 In this article, we focus to study about modified objective function approach for multiobjective optimization problem with vanishing constraints. An equivalent η-approximated multiobjective optimization problem is constructed by a modification of the objective function in the original considered optimization problem. Furthermore, we discuss saddle point criteria for the aforesaid problem. Moreover, we present some examples to verify the established results. 参考文献 | 相关文章 | 计量指标

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RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE 梁载涛, 杨艳娟 数学物理学报(英文版). 2019 (2):  395-402.  DOI: 10.1007/s10473-019-0205-7 摘要 ( 44 )   RICH HTML PDF   收藏 In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature. 参考文献 | 相关文章 | 计量指标

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TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS 袁海荣 数学物理学报(英文版). 2019 (2):  403-412.  DOI: 10.1007/s10473-019-0206-6 摘要 ( 47 )   RICH HTML PDF   收藏 We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws. 参考文献 | 相关文章 | 计量指标

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A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES 任颜波 数学物理学报(英文版). 2019 (2):  413-419.  DOI: 10.1007/s10473-019-0207-5 摘要 ( 50 )   RICH HTML PDF   收藏 In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form holds a.e. for uniformly integrable martingales f = (fn)n≥0 with some constant C > 0, where Φ1, Φ2 are Young functions, wi (i = 1, 2, 3, 4) are weights, and f∞ = fn a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented. 参考文献 | 相关文章 | 计量指标

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ON INTEGRABILITY UP TO THE BOUNDARY OF THE WEAK SOLUTIONS TO A NON-NEWTONIAN FLUID 郭闪闪, 谭忠 数学物理学报(英文版). 2019 (2):  420-428.  DOI: 10.1007/s10473-019-0208-4 摘要 ( 46 )   RICH HTML PDF   收藏 This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equations as The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKⅡ, we show that the density ρ is square integrable up to the boundary. 参考文献 | 相关文章 | 计量指标

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ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION 王长有, 李楠, 周钰谦, 蒲兴成, 李锐 数学物理学报(英文版). 2019 (2):  429-448.  DOI: 10.1007/s10473-019-0209-3 摘要 ( 58 )   RICH HTML PDF   收藏 This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system. 参考文献 | 相关文章 | 计量指标

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LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL 樊继山, 栗付才 数学物理学报(英文版). 2019 (2):  449-460.  DOI: 10.1007/s10473-019-0210-x 摘要 ( 30 )   RICH HTML PDF   收藏 In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals. 参考文献 | 相关文章 | 计量指标

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MIXED VARIATIONAL INEQUALITIES DRIVEN BY FRACTIONAL EVOLUTIONARY EQUATIONS Stanisłw MIGÓRSKI, Shengda ZENG 数学物理学报(英文版). 2019 (2):  461-468.  DOI: 10.1007/s10473-019-0211-9 摘要 ( 46 )   RICH HTML PDF   收藏 The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions. 参考文献 | 相关文章 | 计量指标

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GLOBAL EXISTENCE AND OPTIMAL CONVERGENCE RATES OF SOLUTIONS FOR THREE-DIMENSIONAL ELECTROMAGNETIC FLUID SYSTEM 李银, 位瑞英, 姚正安 数学物理学报(英文版). 2019 (2):  469-490.  DOI: 10.1007/s10473-019-0212-8 摘要 ( 50 )   RICH HTML PDF   收藏 In this article, we study the electromagnetic fluid system in three-dimensional whole space R3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the Lp - Lq estimates for the linearized equations and an elaborate energy method when the L1-norm of the perturbation is bounded. 参考文献 | 相关文章 | 计量指标

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LIOUVILLE TYPE THEOREM FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS Simon SCHULZ 数学物理学报(英文版). 2019 (2):  491-497.  DOI: 10.1007/s10473-019-0213-7 摘要 ( 36 )   RICH HTML PDF   收藏 We show that any smooth solution (u, H) to the stationary equations of magnetohydrodynamics belonging to both spaces L6(R3) and BMO-1(R3) must be identically zero. This is an extension of previous results, all of which systematically required stronger integrability and the additional assumption ▽u, ▽H ∈ L2(R3), i.e., finite Dirichlet integral. 参考文献 | 相关文章 | 计量指标

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LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES 马文秀 数学物理学报(英文版). 2019 (2):  498-508.  DOI: 10.1007/s10473-019-0214-6 摘要 ( 51 )   RICH HTML PDF   收藏 Taking a class of linear (4+1)-dimensional partial differential equations as examples, we would like to show that there exist lump solutions and interaction solutions in (4+1)-dimensions. We will compute abundant lump solutions and interaction solutions to the considered linear (4+1)-dimensional partial differential equations via symbolic computations, and plot three specific solutions with Maple plot tools, which supplements the existing literature on lump, rogue wave and breather solutions and their interaction solutions in soliton theory. 参考文献 | 相关文章 | 计量指标

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RIEMANN-HILBERT PROBLEMS OF A SIX-COMPONENT MKDV SYSTEM AND ITS SOLITON SOLUTIONS 马文秀 数学物理学报(英文版). 2019 (2):  509-523.  DOI: 10.1007/s10473-019-0215-5 摘要 ( 43 )   RICH HTML PDF   收藏 Based on a 4×4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed, through a reduced Riemann-Hilbert problem where an identity jump matrix is taken. 参考文献 | 相关文章 | 计量指标

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VECTORIAL EKELAND VARIATIONAL PRINCIPLE AND CYCLICALLY ANTIMONOTONE EQUILIBRIUM PROBLEMS 邱京辉 数学物理学报(英文版). 2019 (2):  524-544.  DOI: 10.1007/s10473-019-0216-4 摘要 ( 41 )   RICH HTML PDF   收藏 In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle (see Qiu, 2014), we prove a new version of Ekeland variational principle (briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results (no matter scalar-valued case, or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings. 参考文献 | 相关文章 | 计量指标

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NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN 纪正超 数学物理学报(英文版). 2019 (2):  545-550.  DOI: 10.1007/s10473-019-0217-3 摘要 ( 43 )   RICH HTML PDF   收藏 In this paper, we investigate non-zero positive eigenvalues of the Laplacian with Dirichlet boundary condition in an n-dimentional Euclidean space Rn, then we obtain an new upper bound of the (k + 1)-th eigenvalue λk+1, which improve the previous estimate which was obtained by Cheng and Yang, see (1.8). 参考文献 | 相关文章 | 计量指标

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APPROXIMATE SOLUTION OF P-RADICAL FUNCTIONAL EQUATION IN 2-BANACH SPACES Muaadh ALMAHALEBI, Abdellatif CHAHBI 数学物理学报(英文版). 2019 (2):  551-566.  DOI: 10.1007/s10473-019-0218-2 摘要 ( 45 )   RICH HTML PDF   收藏 The aim of this paper is to introduce and solve the p-radical functional equation We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces. 参考文献 | 相关文章 | 计量指标

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BLOW-UP PHENOMENA FOR A CLASS OF GENERALIZED DOUBLE DISPERSION EQUATIONS 狄华斐, 尚亚东 数学物理学报(英文版). 2019 (2):  567-579.  DOI: 10.1007/s10473-019-0219-1 摘要 ( 53 )   RICH HTML PDF   收藏 In this article, we study the blow-up phenomena of generalized double dispersion equations utt - uxx - uxxt + uxxxx - uxxtt = f(ux)x. Under suitable conditions on the initial data, we first establish a blow-up result for the solutions with arbitrary high initial energy, and give some upper bounds for blow-up time T* depending on sign and size of initial energy E(0). Furthermore, a lower bound for blow-up time T* is determined by means of a differential inequality argument when blow-up occurs. 参考文献 | 相关文章 | 计量指标

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A NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC EQUATION VIA DUAL APPROACH 杨先勇, 张薇, 赵富坤 数学物理学报(英文版). 2019 (2):  580-596.  DOI: 10.1007/s10473-019-0220-8 摘要 ( 41 )   RICH HTML PDF   收藏 In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in RN which includes the so-called modified nonlinear Schrödinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution. 参考文献 | 相关文章 | 计量指标

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LARGE TIME BEHAVIOR OF SOLUTION TO NONLINEAR DIRAC EQUATION IN 1+1 DIMENSIONS 张永前, 赵勤 数学物理学报(英文版). 2019 (2):  597-606.  DOI: 10.1007/s10473-019-0221-7 摘要 ( 36 )   RICH HTML PDF   收藏 This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in R1+1. It is shown that the solution will tend to travelling wave solution when time tends to infinity. 参考文献 | 相关文章 | 计量指标

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NUMERICAL ANALYSIS FOR VOLTERRA INTEGRAL EQUATION WITH TWO KINDS OF DELAY 郑伟珊, 陈艳萍 数学物理学报(英文版). 2019 (2):  607-617.  DOI: 10.1007/s10473-019-0222-6 摘要 ( 58 )   RICH HTML PDF   收藏 In this article, we study the Volterra integral equations with two kinds of delay that are proportional delay and nonproportional delay. We mainly use Chebyshev spectral collocation method to analyze them. First, we use variable transformation to transform the equation into an new equation which is defined in [-1, 1]. Then, with the help of Gronwall inequality and some other lemmas, we provide a rigorous error analysis for the proposed method, which shows that the numerical error decay exponentially in L∞ and Lωc2-norm. In the end, we give numerical test to confirm the conclusion. 参考文献 | 相关文章 | 计量指标

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A GENERAL DECAY AND OPTIMAL DECAY RESULT IN A HEAT SYSTEM WITH A VISCOELASTIC TERM Abderrahmane YOUKANA, Salim A. MESSAOUDI, Aissa GUESMIA 数学物理学报(英文版). 2019 (2):  618-626.  DOI: 10.1007/s10473-019-0223-5 摘要 ( 44 )   RICH HTML PDF   收藏 We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes several stability results in the literature. 参考文献 | 相关文章 | 计量指标