费马q-差分微分方程整函数解的增长性研究（英文）

本文研究了费马q-差分微分方程的整函数解的相关问题.利用经典和差分的Nevanlinna理论和函数方程理论的研究方法,获得了q-差分微分方程整函数解增长性的几个结果.     

准晶弹性理论边值问题的可解性

通过给出准晶弹性偏微分方程组边值问题的矩阵表示去定义弱解,利用Korn不等式和函数空间理论证明了这种弱解的存在性与唯一性,从而把经典弹性理论边值问题解的存在性定理推广到准晶弹性理论上,这种理论为发展极其复杂与困难的准晶弹性的偏微分方程的边值问题的数值解提供了一个基础．     

费马q-差分微分方程整函数解的增长性研究

本文研究了费马q-差分微分方程的整函数解的相关问题.利用经典和差分的Nevanlinna理论和函数方程理论的研究方法,获得了q-差分微分方程整函数解增长性的几个结果.     

基于再生核三次样条基底的构造及其应用

将三次样条理论与再生核理论相结合,利用再生核函数巧妙地构造了三次样条函数空间的一组基底.基于三次样条插值的高收敛特点,得到了微分方程边值问题近似解的一种新的求解方法.数值算例展现出算法简单、有效.     

小波在微分方程数值解上的应用

求解微分方程常见的方法包括有限差分、有限元等.近年来,小波理论迅速发展,用小波方法数值解求解微分方程已越来越引起人们的注意.本文引入小波的基本理论,通过将函数及其各阶导数在小波基上的展开,求解微分方程的数值解.     

复域偏微分方程(组)超越整函数解的存在性

文章通过多变量值分布理论研究复偏微分方程与方程组的解,得到一类偏微分方程与一类偏微分方程组有限级超越整函数解的存在性及其形式.同时,我们举例说明了结果是精确的.     

一类复代数微分方程解的解析式

利用亚纯函数的Nevanlinna值分布理论和微分代数知识,研究了一类高阶代数微分方程解的解析式问题,该类高阶微分方程解的解析式被得到.     

亚纯函数系数高阶复域微分方程解的不动点

研究了一类亚纯函数系数的高阶线性微分方程的解的不动点问题,应用值分布的理论和方法,得到了复域微分方程亚纯解的不动点性质.     

C^m中高阶偏微分方程的代数体解

该文利用多复变函数值分布理论和技巧,研究了Cm中高阶偏微分方程的代数体函数解的存在性问题,建立了Cm中高阶偏微分方程的Malmquist型定理.     

Banach空间中非线性刚性Volterra泛函微分方程稳定性分析

获得了Banach空间中非线性刚性Volterra泛函微分方程理论解的一系列稳定性、收缩性及渐近稳定性结果,为非线性刚性常微分方程、延迟微分方程、积分微分方程及实际问题中遇到的其他各种类型的泛函微分方程的解的稳定性分析提供了统一的理论基础.     

EXISTENCE AND DECAY OF WEAK SOLUTIONS TO DEGENERATE DAVEY-STEWARTSON EQUATIONS

In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.     

Remarks on Leray's self‐similar solutions to the 3D magnetohydrodynamic equations

In this note, we examine small self‐similar solutions of the 3D incompressible magnetohydrodynamic equations in homogenous function spaces and show the uniqueness of self‐similar solutions when the velocity field is small in some homogeneous function spaces. This extend the recent results given by C. He and Z. Xin. “On the self‐similar solutions of the magneto‐hydro‐dynamic equations. Acta Mathematica Scientia, série B English Edition 2009; 29 (3): 583–598”. It is a natural way to extend the space widely and improve the previous results. Copyright © 2013 John Wiley & Sons, Ltd.     

RESEARCH ANNOUNCEMENTS：Morrey Regularity of the Solution to the Diri

To study the local regularity of solutions to second orderelliptic partial differential equations, Morrey in ［1］ introduced somefunction spaces, which are called the Morrey spaces today. Since then, manymathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.     

Ekeland's inverse function theorem in graded Fréchet spaces revisited for multifunctions

In this paper, we present some inverse function theorems and implicit function theorems for set-valued mappings between Fréchet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Fréchet spaces with non-smooth data is given.     

A method of numerical solution of functional equations

Approximate solutions of some functional equations as the best approximation of the exact solutions in some suitable spaces have been obtained and some applications given.     

Nontrivial solutions to boundary value problems for semilinear strongly degenerate elliptic differential equations

In this paper we study boundary value problems for semilinear equations involving strongly degenerate elliptic differential operators. Via a Pohozaev??s type identity we show that if the nonlinear term grows faster than some power function then the boundary value problem has no nontrivial solution. Otherwise when the nonlinear term grows slower than the same power function, by establishing embedding theorems for weighted Sobolev spaces associated with the strongly degenerate elliptic equations, then applying the theory of critical values in Banach spaces, we prove that the problem has a nontrivial solution, or even infinite number of solutions provided that the nonlinear term is an odd function.     

Banach空间中一类分数阶微分方程边值问题

研究Banach空间中一类非线性分数阶微分方程边值问题.构建此类方程的Green函数,利用非紧测度和相关的不动点定理,得到了此类方程的mild解存在的几个充分条件,所得结果改进和推广了一些已有的结论.     

On NAVIER-STOKES and KELVIN-VOIGT Equations in Three Dimensions in Interpolation Spaces

We show for the three-dimensional initial-boundary value problem of the NAVIER -STOKES and KELVIN -VOIGT equation over bounded domains and for the corresponding stationary problem the existence of weak solutions in intermediate spaces between some of the usual spaces for weak solutions of the NAVIER -STOKES equations and spaces for the corresponding strong solutions. The proofs yield estimates of the solutions in terms of the data which are supposed to be in appropriate intermediate spaces. The basic ingredients of the proof are well-known results for weak and strong solutions and some nonlinear interpolation arguments.     

Existence and structure results on almost periodic solutions of difference equations

We study the almost periodic solutions of Euler equations and of some more general Difference Equations. We consider two different notions of almost periodic sequences, and we establish some relations between them. We build suitable sequences spaces and we prove some properties of these spaces. We also prove properties of Nemytskii operators on these spaces. We build a variational approach to establish existence of almost periodic solutions as critical points, We obtain existence theorems fornonautonomous linear equations and for an Euler equation with a concave and coercive Lagrangian. We also use a Fixed Point approach to obtain existence results for quasi-linear Difference Equations.     

On global continuability of solutions of infinite-dimensional ordinary differential equations

We prove necessary and sufficient conditions for global in time existence of solutions of ordinary differential equations on infinite dimensional Banach spaces and manifolds under some natural additional hypotheses, in particular, for equations with right-hand sides, given on everywhere dense subsets of phase spaces.