一类非线性二阶常微分方程Dirichlet问题正解的存在性

Existence of positive solutions for a class of nonlinear second-order Dirichlet problem

本文研究了一类非线性二阶常微分方程Dirichlet边值问题{u″-a(t)u+f(t,u)=0,0<t<1,u(0)=u(1)=0正解的存在性,其中f:[0,1]×[0,∞)→[0,∞)连续,a(t):[0,1]→[0,∞)连续,主要结果的证明基于锥拉伸与压缩不动点定理.

In this paper, we study the existence of positive solutions for a class of nonlinear second-order Dirichlet problem where f：[0,1]×[0,∞）→[0,∞）is continuous,a（t）：[0,1]-[0,∞）is continuous. The proof of the main results is based on the fixed-point theorem of cone expansion -compression.