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2018年, 第38卷, 第2期　刊出日期：2018-04-25 上一期    下一期

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ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS Janusz BRZDȨK, Krzysztof CIEPLINSKI 数学物理学报(英文版). 2018 (2):  377-390.  DOI: 10.1016/S0252-9602(18)30755-0 摘要 ( 161 )   RICH HTML PDF   收藏 The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability results concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented. 参考文献 | 相关文章 | 计量指标

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MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN RN 贾慧芳, 李工宝 数学物理学报(英文版). 2018 (2):  391-418.  DOI: 10.1016/S0252-9602(18)30756-2 摘要 ( 121 )   RICH HTML PDF   收藏 In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrödinger-Kirchhoff type -εpM(εp-N ∫RN|▽u|p)△pu + V (x)|u|p-2u=f(u) in RN, where △p is the p-Laplacian operator, 1< p < N, M:R+→ R+ and V:RN → R+ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and LyusternikSchnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation. 参考文献 | 相关文章 | 计量指标

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MULTIPLICITY OF SOLUTIONS OF WEIGHTED (p, q)-LAPLACIAN WITH SMALL SOURCE 宋慧娟, 尹景学, 王泽佳 数学物理学报(英文版). 2018 (2):  419-428.  DOI: 10.1016/S0252-9602(18)30757-4 摘要 ( 71 )   RICH HTML PDF   收藏 In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system -div(h1(x)|▽u|p-2▽u)=d(x)|u|r-2u + Gu(x, u, v) in Ω, -div(h2(x)|▽v|q-2▽v)=f(x)|v|s-2v + Gv(x, u, v) in Ω, u=v=0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, N ≥ 2, 1< r < p < ∞, 1< s < q < ∞; h1(x) and h2(x) are allowed to have "essential" zeroes at some points in Ω; d(x)|u|r-2u and f(x)|v|s-2v are small sources with Gu(x,u, v), Gv(x, u, v) being their high-order perturbations with respect to (u, v) near the origin, respectively. 参考文献 | 相关文章 | 计量指标

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QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM 付静, 蒋达清, 史宁中, Tasawar HAYAT, Ahmed ALSAEDI 数学物理学报(英文版). 2018 (2):  429-440.  DOI: 10.1016/S0252-9602(18)30758-6 摘要 ( 63 )   RICH HTML PDF   收藏 This article addresses a stochastic ratio-dependent predator-prey system with Leslie-Gower and Holling type Ⅱ schemes. Firstly, the existence of the global positive solution is shown by the comparison theorem of stochastic differential equations. Secondly, in the case of persistence, we prove that there exists a ergodic stationary distribution. Finally, numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings. 参考文献 | 相关文章 | 计量指标

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SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES 魏明权, 燕敦验 数学物理学报(英文版). 2018 (2):  441-449.  DOI: 10.1016/S0252-9602(18)30759-8 摘要 ( 73 )   RICH HTML PDF   收藏 In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI(Gn) are obtained. 参考文献 | 相关文章 | 计量指标

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CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM 段火元, 马俊华 数学物理学报(英文版). 2018 (2):  450-470.  DOI: 10.1016/S0252-9602(18)30760-4 摘要 ( 118 )   RICH HTML PDF   收藏 On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming (bi)linear macroelements or (bi)quadratic elements, and the rotation by conforming (bi)linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results. 参考文献 | 相关文章 | 计量指标

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A NOTE ON MALMQUIST-YOSIDA TYPE THEOREM OF HIGHER ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS 张建军, 廖良文 数学物理学报(英文版). 2018 (2):  471-478.  DOI: 10.1016/S0252-9602(18)30761-6 摘要 ( 123 )   RICH HTML PDF   收藏 In this article, we give a simple proof of Malmquist-Yosida type theorem of higher order algebraic differential equations, which is different from the methods as that of Gackstatter and Laine[2], and Steinmetz[12]. 参考文献 | 相关文章 | 计量指标

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A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS 盛洲, 袁功林, 崔曾如 数学物理学报(英文版). 2018 (2):  479-496.  DOI: 10.1016/S0252-9602(18)30762-8 摘要 ( 83 )   RICH HTML PDF   收藏 It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving unconstrained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient. 参考文献 | 相关文章 | 计量指标

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MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH 廖家锋, 蒲洋, 唐春雷 数学物理学报(英文版). 2018 (2):  497-518.  DOI: 10.1016/S0252-9602(18)30763-X 摘要 ( 100 )   RICH HTML PDF   收藏 In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered, ???20180209??? where Ω ⊂ RN(N ≥ 3) is an open bounded domain with smooth boundary, 1< q < 2, λ > 0.2*=2N/N-2 is the critical Sobolev exponent, f ∈L 2*/(2*-q) (Ω) is nonzero and nonnegative, and g ∈ C(Ω) is a positive function with k local maximum points. By the Nehari method and variational method, k +1 positive solutions are obtained. Our results complement and optimize the previous work by Lin[MR2870946, Nonlinear Anal. 75(2012) 2660-2671]. 参考文献 | 相关文章 | 计量指标

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CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM 袁益让, 程爱杰, 羊丹平, 李长峰, 杨青 数学物理学报(英文版). 2018 (2):  519-545.  DOI: 10.1016/S0252-9602(18)30764-1 摘要 ( 70 )   RICH HTML PDF   收藏 The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in l2 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems. 参考文献 | 相关文章 | 计量指标

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TWO DIMENSIONAL MELLIN TRANSFORM IN QUANTUM CALCULUS Kamel BRAHIM, Latifa RIAHI 数学物理学报(英文版). 2018 (2):  546-560.  DOI: 10.1016/S0252-9602(18)30765-3 摘要 ( 99 )   RICH HTML PDF   收藏 In this article, we introduce the two dimensional Mellin transform Mq (f)(s, t), give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform. 参考文献 | 相关文章 | 计量指标

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FINITE-TIME H∞ CONTROL FOR A CLASS OF MARKOVIAN JUMPING NEURAL NETWORKS WITH DISTRIBUTED TIME VARYING DELAYS-LMI APPROACH P. BASKAR, S. PADMANABHAN, M. SYED ALI 数学物理学报(英文版). 2018 (2):  561-579.  DOI: 10.1016/S0252-9602(18)30766-5 摘要 ( 74 )   RICH HTML PDF   收藏 In this article, we investigates finite-time H∞ control problem of Markovian jumping neural networks of neutral type with distributed time varying delays. The mathematical model of the Markovian jumping neural networks with distributed delays is established in which a set of neural networks are used as individual subsystems. Finite time stability analysis for such neural networks is addressed based on the linear matrix inequality approach. Numerical examples are given to illustrate the usefulness of our proposed method. The results obtained are compared with the results in the literature to show the conservativeness. 参考文献 | 相关文章 | 计量指标

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NUMERICAL SIMULATIONS FOR A VARIABLE ORDER FRACTIONAL CABLE EQUATION A. M. NAGY, N. H. SWEILAM 数学物理学报(英文版). 2018 (2):  580-590.  DOI: 10.1016/S0252-9602(18)30767-7 摘要 ( 93 )   RICH HTML PDF   收藏 In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the RiemannLiouville and the Grünwald-Letnikov sense. The stability analysis of the proposed technique is discussed. Numerical results are provided and compared with exact solutions to show the accuracy of the proposed technique. 参考文献 | 相关文章 | 计量指标

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EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS 李扬荣, 佘连兵, 尹金艳 数学物理学报(英文版). 2018 (2):  591-609.  DOI: 10.1016/S0252-9602(18)30768-9 摘要 ( 81 )   RICH HTML PDF   收藏 A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynamical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force. 参考文献 | 相关文章 | 计量指标

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CONVERGENCE OF HYBRID VISCOSITY AND STEEPEST-DESCENT METHODS FOR PSEUDOCONTRACTIVE MAPPINGS AND NONLINEAR HAMMERSTEIN EQUATIONS Yekini SHEHU, Olaniyi. S. IYIOLA 数学物理学报(英文版). 2018 (2):  610-626.  DOI: 10.1016/S0252-9602(18)30769-0 摘要 ( 86 )   RICH HTML PDF   收藏 In this article, we first introduce an iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping (assuming existence) and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a nonlinear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method. 参考文献 | 相关文章 | 计量指标

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DIFFUSION VANISHING LIMIT OF THE NONLINEAR PIPE MAGNETOHYDRODYNAMIC FLOW WITH FIXED VISCOSITY 吴忠林, 王术 数学物理学报(英文版). 2018 (2):  627-642.  DOI: 10.1016/S0252-9602(18)30770-7 摘要 ( 64 )   RICH HTML PDF   收藏 We establish magnetic diffusion vanishing limit of the nonlinear pipe Magnetohydrodynamic flow by the mathematical validity of the Prandtl boundary layer theory with fixed viscosity. The convergence is verified under various Sobolev norms, including the L∞(L2) and L∞(H1) norm. 参考文献 | 相关文章 | 计量指标

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A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES 刘春燕, 张子厚, 周宇 数学物理学报(英文版). 2018 (2):  643-650.  DOI: 10.1016/S0252-9602(18)30771-9 摘要 ( 97 )   RICH HTML PDF   收藏 In this article, we prove the following results:(1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set. 参考文献 | 相关文章 | 计量指标

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THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM 张磊, 刘斌 数学物理学报(英文版). 2018 (2):  651-672.  DOI: 10.1016/S0252-9602(18)30772-0 摘要 ( 63 )   RICH HTML PDF   收藏 This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton (gμHS2) system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative (gμHS2) system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative (gμHS2) system, we show that the semi-group of the solution operator {S(t)}t ≥ 0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S(t)}t ≥ 0 possesses a global attractor in the Sobolev space H2(S)×H2(S). 参考文献 | 相关文章 | 计量指标

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LIOUVILLE THEOREM FOR CHOQUARD EQUATION WITH FINITE MORSE INDICES 赵晓军 数学物理学报(英文版). 2018 (2):  673-680.  DOI: 10.1016/S0252-9602(18)30773-2 摘要 ( 89 )   RICH HTML PDF   收藏 In this article, we study the nonexistence of solution with finite Morse index for the following Choquard type equation -△u=∫RN (|u(y)|p)/(|x-y|α)dy|u(x)|p-2u(x) in RN, where N ≥ 3, 0< α < min{4, N}. Suppose that 2< p < (2N-α)/(N-2), we will show that this problem does not possess nontrivial solution with finite Morse index. While for p=(2N-α)/(N-2), if i(u) < ∞, then we have ∫RN ∫RN (|u(x)|p|u(y)|p)/(|x-y|α) dxdy < ∞ and ∫RN|▽u|2 dx=∫RN ∫RN(|u(x)|p|u(y)|p)/(|x-y|α dxdy. 参考文献 | 相关文章 | 计量指标

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SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS 韩月才, 孙一芳 数学物理学报(英文版). 2018 (2):  681-694.  DOI: 10.1016/S0252-9602(18)30774-4 摘要 ( 88 )   RICH HTML PDF   收藏 The local existence and uniqueness of the solutions to backward stochastic differential equations(BSDEs, in short) driven by both fractional Brownian motions with Hurst parameter H∈(1/2,1) and the underlying standard Brownian motions are studied. The generalization of the Itô formula involving the fractional and standard Brownian motions is provided. By theory of Malliavin calculus and contraction mapping principle, the local existence and uniqueness of the solutions to BSDEs driven by both fractional Brownian motions and the underlying standard Brownian motions are obtained. 参考文献 | 相关文章 | 计量指标

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ON A CLASS OF DOUGLAS FINSLER METRICS 朱红梅 数学物理学报(英文版). 2018 (2):  695-708.  DOI: 10.1016/S0252-9602(18)30775-6 摘要 ( 82 )   RICH HTML PDF   收藏 In this article, we study a class of Finsler metrics called general (α, β)-metrics, which are defined by a Riemannian metric α and a 1-form β. We determine all of Douglas general (α, β)-metrics on a manifold of dimension n > 2. 参考文献 | 相关文章 | 计量指标

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STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL Rakesh KUMAR, Anuj Kumar SHARMA, Kulbhushan AGNIHOTRI 数学物理学报(英文版). 2018 (2):  709-732.  DOI: 10.1016/S0252-9602(18)30776-8 摘要 ( 117 )   RICH HTML PDF   收藏 In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage (time delay) is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period (time delay, τ) passes through a critical value. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included. 参考文献 | 相关文章 | 计量指标

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EXISTENCE AND BLOW-UP BEHAVIOR OF CONSTRAINED MINIMIZERS FOR SCHRÖDINGER-POISSON-SLATER SYSTEM 朱新才 数学物理学报(英文版). 2018 (2):  733-744.  DOI: 10.1016/S0252-9602(18)30777-X 摘要 ( 83 )   RICH HTML PDF   收藏 In this article, we study constrained minimizers of the following variational problem e(ρ):=???20180223??? E(u), ρ > 0, where E(u) is the Schrödinger-Poisson-Slater (SPS) energy functional E(u):=1/2 ∫R3|▽u(x)|2dx -1/4 ∫R3 ∫R3 (u2|(y)u2(x))/(|x-y|)dydx -1/p ∫R3|u(x)|pdx in R3, and p ∈ (2, 6). We prove the existence of minimizers for the cases 2< p < 10/3, ρ > 0, and p=10/3, 0< ρ < ρ*, and show that e(ρ)=-∞ for the other cases, where ρ*=||φ||22 and φ(x) is the unique (up to translations) positive radially symmetric solution of -△u + u=u7/3 in R3. Moreover, when e(ρ*)=-∞, the blow-up behavior of minimizers as ρ ↗ ρ* is also analyzed rigorously. 参考文献 | 相关文章 | 计量指标