非线性m点边值问题正解的新结果

New results for positive solutions of nonlinear m-point boundary value problem

本文研究非线性m点边值问题u″(t)+a(t)f(u)=0,t∈(0,1)u′(0)=0,u(1)=^m-2∑i=1αiu(ξi)正解的存在性.利用Leray-Schauder不动点定理,本文获得了问题正解的存在性条件.这个条件弱化了已有的相关结果.

In this paper, we investigate the existence of positive solutions for the following second-order nonlinear m-point boundary value problem:u″(t)+a(t)f(u)=0,t∈(0,1)u′(0)=0,u(1)=^m-2∑i=1αiu(ξi) By using the Leray-Schauder fixed point theorem,we give some sufficient conditions for the existence of positive solutions,which improve the known results.