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2020年, 第40卷, 第1期　刊出日期：2020-02-25 上一期   

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HILBERT PROBLEM 15 AND NONSTANDARD ANALYSIS (I) 李邦河 数学物理学报(英文版). 2020 (1):  1-15.  DOI: 10.1007/s10473-020-0101-4 摘要 ( 126 )   RICH HTML PDF   收藏 In this article, we consider the following coupled fractional nonlinear Schr?dinger system in $\mathbb{R}^{N}$ $$\left\{ \begin{array}{l} {\left( { - \Delta } \right)^s}u + P\left( x \right)u = {\mu _1}{\left| u \right|^{2p - 2}}u + \beta {\left| u \right|^p}{\left| u \right|^{p - 2}}u,\;\;\;x \in {{\mathbb{R}}^N},\\{\left( { - \Delta } \right)^s}v + Q\left( x \right)v = {\mu _2}{\left| v \right|^{2p - 2}}v + \beta {\left| v \right|^p}{\left| v \right|^{p - 2}}v,\;\;\;\;\;x \in {{\mathbb{R}}^N},\\u,\;\;v \in {H^s}\left( {{{\mathbb{R}}^N}} \right),\end{array} \right.$$ where $N≥2, 0 < s < 1, 1 < p < \frac{N}{N-2s},\mu_1>0, \mu_2>0$ and $\beta \in \mathbb{R}$ is a coupling constant. We prove that it has infinitely many non-radial positive solutions under some additional conditions on $P(x), Q(x), p$ and $\beta$. More precisely, we will show that for the attractive case, it has infinitely many non-radial positive synchronized vector solutions, and for the repulsive case, infinitely many non-radial positive segregated vector solutions can be found, where we assume that $P(x)$ and $Q(x)$ satisfy some algebraic decay at infinity. 参考文献 | 相关文章 | 计量指标

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INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA 王春花, 周静 数学物理学报(英文版). 2020 (1):  16-34.  DOI: 10.1007/s10473-020-0102-3 摘要 ( 151 )   RICH HTML PDF   收藏 In this paper, we consider the following coupled Schr?dinger system with χ(2) nonlinearities which arises from second-harmonic generation in quadratic media. Here V1(x) and V2(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V1(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type. 参考文献 | 相关文章 | 计量指标

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COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL 蒋操, 董兴堂, 周泽华 数学物理学报(英文版). 2020 (1):  35-44.  DOI: 10.1007/s10473-020-103-2 摘要 ( 94 )   RICH HTML PDF   收藏 In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained. 参考文献 | 相关文章 | 计量指标

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THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS 李金霞, 李宝德, 何建勋 数学物理学报(英文版). 2020 (1):  45-58.  DOI: 10.1007/s10473-020-104-1 摘要 ( 122 )   RICH HTML PDF   收藏 Let T be an anisotropic Calderón-Zygmund operator and φ : Rn×[0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function with φ(x, ·) being an Orlicz function and φ(·, t) being a Muckenhoupt A∞(A) weight. In this paper, our goal is to study two boundedness theorems for commutators of anisotropic Calderón-Zygmund operators. Precisely, when b ∈ BMOw(Rn, A) (a proper subspace of anisotropic bounded mean oscillation space BMO(Rn, A)), the commutator [b, T] is bounded from anisotropic weighted Hardy space Hw1(Rn, A) to weighted Lebesgue space Lw1(Rn) and when b ∈ BMO(Rn) (bounded mean oscillation space), the commutator [b, T] is bounded on Musielak-Orlicz space Lφ(Rn), which are extensions of the isotropic setting. 参考文献 | 相关文章 | 计量指标

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GROUND STATES FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH 李全清, 王文波, 滕凯民, 吴鲜 数学物理学报(英文版). 2020 (1):  59-74.  DOI: 10.1007/s10473-020-0105-0 摘要 ( 50 )   RICH HTML PDF   收藏 In this article, we study the following fractional Schrödinger equation with electromagnetic fields and critical growth (-△)Asu + V (x)u = |u|2s*-2u + λf(x,|u|2)u, x ∈ RN, where (-△)As is the fractional magnetic operator with 0 < s < 1, N > 2s, λ > 0, 2s* = 2N/(N-2s), f is a continuous function, V ∈ C(RN, R) and A ∈ C(RN, RN) are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method. 参考文献 | 相关文章 | 计量指标

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MULTIPLE JEEPS PROBLEM WITH CONTAINER RESTRICTION 华香颖 数学物理学报(英文版). 2020 (1):  75-89.  DOI: 10.1007/s10473-020-0106-z 摘要 ( 40 )   RICH HTML PDF   收藏 Jeep problem is a kind of model of logistics in extreme situation, which has application in exploration and aircraft problems. The optimal distance and driving strategy of multiple jeeps problem are known. We consider multiple jeeps problem with container restriction, which is more complicated in the proof of feasibility and optimality of a driving strategy. We investigate when it can achieve the same optimal distance as without restriction. Based on the non-restricted optimal distance, a new driving strategy is proposed. We provide the necessary and sufficient condition to ensure the feasibility of the strategy, and obtain the maximal feasible distance. 参考文献 | 相关文章 | 计量指标

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THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION 李工宝, 牛亚慧 数学物理学报(英文版). 2020 (1):  90-112.  DOI: 10.1007/s10473-020-0107-y 摘要 ( 67 )   RICH HTML PDF   收藏 In the present paper, we consider the nonlocal Kirchhoff problem - (ε2a + εb∫R3 |▽u|2)△u + u = Q(x)up, u > 0 in R3, where a, b > 0, 1 < p < 5 and ε > 0 is a parameter. Under some assumptions on Q(x), we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method, respectly. 参考文献 | 相关文章 | 计量指标

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N-SOLITON SOLUTION OF THE KUNDU-TYPE EQUATION VIA RIEMANN-HILBERT APPROACH 温丽丽, 张宁, 范恩贵 数学物理学报(英文版). 2020 (1):  113-126.  DOI: 10.1007/s10473-020-0108-x 摘要 ( 56 )   RICH HTML PDF   收藏 In this article, we focus on investigating the Kundu-type equation with zero boundary condition at infinity. Based on the analytical and symmetric properties of eigenfunctions and spectral matrix of its Lax pair, a Riemann-Hilbert problem for the initial value problem of the Kundu-type equation is constructed. Further through solving the regular and nonregular Riemann-Hilbert problem, a kind of general N-soliton solution of the Kundu-type equation are presented. As special cases of this result, the N-soliton solution of the Kaup-Newell equation, Chen-Lee-Liu equation, and Gerjikov-Ivanov equation can be obtained respectively by choosing different parameters. 参考文献 | 相关文章 | 计量指标

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HIGHER-ORDER NON-SYMMETRIC DUALITY FOR NONDIFFERENTIABLE MINIMAX FRACTIONAL PROGRAMS WITH SQUARE ROOT TERMS SONALI, Vikas SHARMA, Navdeep KAILEY 数学物理学报(英文版). 2020 (1):  127-140.  DOI: 10.1007/s10473-020-0109-9 摘要 ( 44 )   RICH HTML PDF   收藏 In this paper, we emphasize on a nondifferentiable minimax fractional programming (NMFP) problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions. We provide a nontrivial illustration of a function which belongs to the class of higher-order B-(p,r)-invex but not in the class of second-order B-(p,r)-invex functions already existing in literature. An example of finding a minimax solution of NMFP problem by using higher-order B-(p,r)-invex functions has also been given. Various known results are discussed as particular cases. 参考文献 | 相关文章 | 计量指标

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EXISTENCE AND STABILITY RESULTS FOR GENERALIZED FRACTIONAL DIFFERENTIAL EQUATIONS A. BEN MAKHLOUF, D. BOUCENNA, M. A. HAMMAMI 数学物理学报(英文版). 2020 (1):  141-154.  DOI: 10.1007/s10473-020-0110-3 摘要 ( 57 )   RICH HTML PDF   收藏 In this paper, a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of order α (1 < α < 2) are given. The main results are obtained by using Krasnoselskii's fixed point theorem in a weighted Banach space. Two examples are given to demonstrate the validity of the proposed results. 参考文献 | 相关文章 | 计量指标

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GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS 于佳利, 尚亚东, 狄华斐 数学物理学报(英文版). 2020 (1):  155-169.  DOI: 10.1007/s10473-020-0111-2 摘要 ( 43 )   RICH HTML PDF   收藏 This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms utt - △u - △ut - △utt + ∫0tg(t - s)△u(s)ds + ut|ut|m-2=u|u|p-2 with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition. 参考文献 | 相关文章 | 计量指标

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OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS 李静伟, 刘国欣, 赵锦艳 数学物理学报(英文版). 2020 (1):  170-198.  DOI: 10.1007/s10473-020-0112-1 摘要 ( 68 )   RICH HTML PDF   收藏 This paper concerns an optimal dividend-penalty problem for the risk models with surplus-dependent premiums. The objective is to maximize the difference of the expected cumulative discounted dividend payments received until the moment of ruin and a discounted penalty payment taken at the moment of ruin. Since the value function may be not smooth enough to be the classical solution of the HJB equation, the viscosity solution is involved. The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation and the optimal dividend-penalty strategy has a band structure. Finally, some numerical examples with gamma distribution for the claims are analyzed. 参考文献 | 相关文章 | 计量指标

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LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS Ioannis K. ARGYROS, Yeol Je CHO, Santhosh GEORGE, 肖义彬 数学物理学报(英文版). 2020 (1):  199-210.  DOI: 10.1007/s10473-020-0113-0 摘要 ( 45 )   RICH HTML PDF   收藏 The paper develops the local convergence of Inexact Newton-Like Method (INLM) for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The obtained results compare favorably with earlier ones such as [7, 13, 14, 18, 19]. A numerical example is also provided 参考文献 | 相关文章 | 计量指标

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HERMITIAN-EINSTEIN METRICS FOR HIGGS BUNDLES OVER COMPLETE HERMITIAN MANIFOLDS 刘德斌, 张攀 数学物理学报(英文版). 2020 (1):  211-225.  DOI: 10.1007/s10473-020-0114-z 摘要 ( 39 )   RICH HTML PDF   收藏 In this paper, we solve the Dirichlet problem for the Hermitian-Einstein equations on Higgs bundles over compact Hermitian manifolds. Then we prove the existence of the Hermitian-Einstein metrics on Higgs bundles over a class of complete Hermitian manifolds. 参考文献 | 相关文章 | 计量指标

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EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS Alberto CABADA, Nikolay DIMITROV 数学物理学报(英文版). 2020 (1):  226-236.  DOI: 10.1007/s10473-020-0115-y 摘要 ( 55 )   RICH HTML PDF   收藏 The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions. Before to do this, we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for. Moreover, we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems. Once we have the general existence result, we deduce, as a particular case, the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions. 参考文献 | 相关文章 | 计量指标

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THE ENERGY CONSERVATIONS AND LOWER BOUNDS FOR POSSIBLE SINGULAR SOLUTIONS TO THE 3D INCOMPRESSIBLE MHD EQUATIONS Jae-Myoung KIM 数学物理学报(英文版). 2020 (1):  237-244.  DOI: 10.1007/s10473-020-0116-x 摘要 ( 70 )   RICH HTML PDF   收藏 In this note, we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations. Moreover, we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations. 参考文献 | 相关文章 | 计量指标

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COMPLEX INTERPOLATION OF NONCOMMUTATIVE HARDY SPACES ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRAS 吐尔德·别克, Kordan N. OSPANOV 数学物理学报(英文版). 2020 (1):  245-260.  DOI: 10.1007/s10473-020-0117-9 摘要 ( 60 )   RICH HTML PDF   收藏 We proved a complex interpolation theorem of noncommutative Hardy spaces associated with semi-finite von Neumann algebras and extend the Riesz type factorization to the semi-finite case. 参考文献 | 相关文章 | 计量指标

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GLOBAL SIMPLE WAVE SOLUTIONS TO A KIND OF TWO DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS 刘见礼, 薛杰 数学物理学报(英文版). 2020 (1):  261-271.  DOI: 10.1007/s10473-020-0118-8 摘要 ( 60 )   RICH HTML PDF   收藏 This paper is concerned with the simple waves of a kind of two dimensional hyperbolic system of conservation laws, which can be obtained from the two dimensional relativistic membrane equation in Minkowski space. Using wave decomposition method, we get that a flow adjacent to a nonconstant state can be a global simple wave. Furthermore, the flow is covered by three families of characteristics, in which the first family of characteristics is straight and the others are curved, which is different to the almost related results. 参考文献 | 相关文章 | 计量指标

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BOUNDEDNESS OF MULTILINEAR LITTLEWOOD-PALEY OPERATORS ON AMALGAM-CAMPANATO SPACES 李翔, 骞君, 燕敦验 数学物理学报(英文版). 2020 (1):  272-292.  DOI: 10.1007/s10473-020-0119-7 摘要 ( 94 )   RICH HTML PDF   收藏 In this paper, we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function, multilinear Lusin’s area integral and multilinear Littlewood-Paley gλ*-function. Furthermore, norm inequalities of the above operators hold on the corresponding Amalgam-Campanato spaces. 参考文献 | 相关文章 | 计量指标