分数阶p-Laplacian Kirchhoff型问题正解的存在性

研究了分数阶p-Laplacian Kirchhoff方程,运用变分法和截断函数理论,证明了在一定条件下具有消失Kirchhoff项的分数阶p-Laplacian问题正解的存在性和多重性.     

一类具有p-Laplacian算子的分数阶差分方程边值问题的正解

该文研究一类具有p-Laplacian算子的分数阶差分方程边值问题.借助离散型Jensen不等式,考虑该问题与相应的不带有p-Laplacian算子的分数阶差分方程边值问题之间的关系,并运用不动点指数理论获得该问题正解的存在性.     

一类分数阶p-Laplacian差分方程边值问题正解的存在性北大核心CSCD

研究一类带p-Laplacian算子的分数阶差分方程边值问题.利用格林函数的特征性质、压缩映射原理及锥上的不动点定理等非线性方法,获得了该分数阶pLaplacian差分方程边值问题解的唯一性及正解的存在性条件,举例说明了所得结论的正确性.     

一类分数阶p-Laplacian差分方程边值问题正解的存在性

研究一类带p-Laplacian算子的分数阶差分方程边值问题.利用格林函数的特征性质、压缩映射原理及锥上的不动点定理等非线性方法,获得了该分数阶pLaplacian差分方程边值问题解的唯一性及正解的存在性条件,举例说明了所得结论的正确性.     

含p-Laplacian算子的分数阶脉冲微分方程边值问题的解

讨论了一类带有p-Laplacian算子的分数阶脉冲微分方程的边值问题,运用不动点定理给出了具p-Laplacian算子的分数阶脉冲微分方程边值问题解存在的充分条件,最后给出实例加以验证.     

一类具有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在唯一性

该文研究了一类具有p-Laplacian算子的非线性Caputo分数阶微分方程反周期边值问题解的存在唯一性.首先,利用分数阶微分方程和反周期边值条件给出了该边值问题的Green函数,然后利用p-Laplacian算子的性质和Banach压缩映射原理得到该边值问题解的存在唯一性结论,最后给出两个例子验证结论的合理性.值得一提的是此文研究的微分方程的反周期边值条件是带有Caputo分数阶微分.     

具有脉冲效应的分数阶p-Laplacian方程耦合系统的可解性（英文）

本文研究了一类具有脉冲效应的分数阶p-Laplacian方程耦合系统的问题.利用变分方法,获得了该系统解存在的一些新结果.在证明过程中,弱化了系统中变系数和非线性项的条件,推广了已有结果.     

分数阶p-Laplacian系统两点边值问题的解

利用Schaefer不动点定理研究了分数阶p-Laplacian系统两点边值问题解的存在性,通过将系统转化为算子方程,在非线性项满足一定增长性的条件下得到了系统至少存在一个解的充分条件,并给出了相关的应用.     

R~n上加权分数阶p-Laplacian的特征值问题（英文）

本文研究一类R~n上加权分数阶p-Laplacian的特征值问题,得到特征值和特征函数的一些性质.     

一类含p-Laplacian算子的分数阶时滞微分方程无穷多点边值问题的正解

主要研究一类含有p-Laplacian算子和时滞的分数阶微分方程的无穷多点边值问题.先构造Green函数并分析其性质,再利用p-Laplacian算子的性质和Banach压缩映射原理,得到这类边值问题正解存在唯一的一些新结果.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].