有序Banach空间非线性Robin边值问题解的存在性

Existence of Solutions for Nonlinear Robin Boundary Value Problems in Banach Spaces

讨论了有序Banach空间E中的非线性Robin边值问题:-u″(t)=f(t,u(t)),0≤t≤1,u(0)=u′(1)=θ解的存在性,其中f:[0,1]×E→E连续。在不假定f满足非紧性测度条件及上下解存在的情形下,通过算子谱理论与半序方法获得了解的存在性结果。

The existence of solutions for nonlinear Robin boundary value problem-u″（t）=f（t,u（t））0≤t≤1,u（0）=u′（1）=θ in ordered Banach spaces E was discussed, where f：[0,1]×E→E is continuous, neither using noncompactness measure condition nor assuming the existence of upper and lower solutions, the existence results of solutions are obtained by employing spectral analysis and semi-order method.