Two positive nontrivial solutions for a class of semilinear elliptic variational systems

We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter's localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray-Schauder boundary condition is also involved.     

一类非局部Cahn-Hilliard方程弱解的存在唯一性

研究一类对流非局部Cahn-Hilliard方程的Neumann问题.通过一致Schauder估计和Leray-Schauder不动点定理,得到了该问题经典解的存在唯一性.进而,利用弱收敛方法得到了该问题弱解的存在唯一性.     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

Exceptional family of elements for general order complementarity problems

The notion of exceptional family of elements for general order complementarity problems in Banach spaces will be introduced. It will be shown that for general order complementarity problems defined by completely continuous fields the problem has either a solution or an exceptional family of elements. Finite dimensional examples and an application to integral operators will be given.     

一类椭圆型随机偏微分方程弱解的存在性

设$D$是$R^N$ ($N>1$)中有界开集,$(\Omega, {\cal F}, P)$是一个完备的概率空间.该文研究了下列随机边值问题弱解的存在性问题\[\left\{\begin{array}{ll}-{\rm div} A(x,\omega,u, \nabla u)=f(x,\omega, u),\,\, &;(x,\omega)\in D\times \Omega,\\u=0, &;(x,\omega)\in \partial D\times \Omega,\end{array}\right.\]其中, div与 $\nabla $ 表示仅对 $x$求微分. 首先,作者引入了弱解的概念; 然后,作者转化随机问题为高维确定性问题;最后,作者证明了该问题弱解的存在性.     

Some existence results for a simplified two fluid system in plasma theory

In this paper, we consider a simplified two fluid system in plasma theory. Some multiple existence results for this system are obtained by variational methods and topological degree methods.     

Positive solutions of Neumann problems with singularities

In this paper, we study the existence of positive solutions to second order singular equations with Neumann boundary conditions. The proof of the main result relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique.     

线性增长限制下一类三阶边值问题的可解性

考察了一类含一阶和二阶导数的三阶边值问题的可解性.非线性项f满足线性增长的限制.通过构造适当的Banach空间并利用Leray-Schauder非线性抉择证明了一个存在定理.     

加权p-Laplace方程解的整体分叉问题

该文利用指标理论，谱理论以及标准分叉定理，研究了加权索伯列夫空间中的p Laplace方程初值问题的解的整体分叉现象。     

Existence of pseudo-almost automorphic solutions for nonlinear differential equations

In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form x＇（t） = f（t,x（t）） ＋ λg（t,x（t））, where f,g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.