有序Banach空间非线性二阶边值问题解的存在性

Existence of solutions for nonlinear second order boundary value problems in ordered Banach spaces

讨论了有序Banach空间E中的非线性二阶边值问题-u″(t)=f(t,u(t)), 0≤t≤1,u(0)=u(1)=θ解的存在性,其中f:[0,1]×EE连续.我们在不假定f满足非紧性测度条件及上下解存在的情形下,用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 second order boundary value problem -u″(t)=f(t,u(t)),0≤t≤1, u(0)=u(1)=θ is discussed in ordered Banach spaces,where f:[0,1]×EE 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.