二阶两点边值问题正解的存在性

Positive Solutions of Second Order Boundary Value Problem

讨论了二阶非线性边值问题-u″(t)+bu′(t)+au(t)=f(t,u(t)),t∈[0,1]u(0)=u(1)=0正解的存在性,其中f∶[0,1]×R+→R+为连续函数.利用锥上的不动点理论,获得了正解存在的最优结果.

This paper studies the existence of positive solutions for the second order boundary value problem {-u″（t）＋bu′（t）＋au（t）=f（t,u（t））,t∈[0,1];u（0）=u（1）0 where f：[0,1]×R＋→R＋ is continuous. The existence of positive solutions is obtained by applying the fixed-point theorem of cone map.