理论数学  >> Vol. 4 No. 5 (September 2014)

一类非线性椭圆方程组三个正解的存在性
Existence of Three Positive Solutions for a Class of Nonlinear Elliptic Systems

DOI: 10.12677/PM.2014.45029, PDF, HTML, 下载: 2,200  浏览: 6,231  科研立项经费支持

作者: 魏公明, 陈雨彤, 张兴丽:上海理工大学理学院数学系,上海

关键词: 非线性椭圆方程组正径向解锥上不动点定理Nonlinear Elliptic System Positive Radial Solution Fixed Point Theorem on Cones

摘要: 受对单个方程多解的存在性的研究的启发,本文研究具有非齐次边界条件的非线性椭圆方程组的存在性及多解性。由锥上Guo-Krasnoselskii不动点定理,本文证明了一类椭圆型方程组至少存在三个正解。
Abstract: Motivated by existence of solutions of single equation, in this paper we study the existence of mul-tiple solutions of a class of nonlienar elliptic systems with nonhomogeneous boundary conditions. Using Guo-Krasnoselski’s fixed point theorem on cones, we prove that there exist at least three positive solutions for this class of nonlinear elliptic systems.

文章引用: 魏公明, 陈雨彤, 张兴丽. 一类非线性椭圆方程组三个正解的存在性[J]. 理论数学, 2014, 4(5): 201-207. http://dx.doi.org/10.12677/PM.2014.45029

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