有序Banach空间非线性Neumann边值问题解的存在性

Existence of Solutions to Nonlinear Neumann Boundary Value Problems in Banach Spaces

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

Under the condition of neither using noncompactness measure nor assuming the existence of upper and lower solutions,by semi-order method,the existence of solutions for nonlinear Neumann boundary value problem-u″（t）=f（t,u（t））,0≤t≤1,u′（0）=u′（1）=θ is obtained.Wheref：×E→E is continuous.