关于二阶非线性方程组的正解

Positive Solutions for Second Order Nonlinear Ordinary Differential Systems

本文主要利用Krasnosel′skii不动点定理,在适当的条件下,当λ>0和μ>0时,给出下面方程组的一个和多个正解的存在性结果:{x″(t)+λa(t)f(x(t),y(t))=0 t∈[0,1] y″(t)+μb(t)g(x(t),y(t))=0 t∈[0,1] x(0)=x′(1)=y(0)=y′(1)=0本文还推导了Green函数,研究了它的性质,从而得到有关一个和多个正解的存在性结果.

In this paper,using Krasnosel′skii fixed point theorem and under suitable conditions,we present the existence of single and multiple positive solutions to the following systems：{x″（t）＋λa（t）f（x（t）,y（t））=0 t∈y″（t）＋μb（t）g（x（t）,y（t））=0 t∈x（0）=x′（1）=y（0）=y′（1）=0where λ0,μ0.In addition,the Green＇s function is deduced and its properties is considered for establishing a new cone and using fixed point theorem.