具有非局部积分边界条件的完全二阶边值问题解的存在性

Existence of solutions for fully second-order boundary value problem with nonlocal integral condition

应用压缩映像原理和Leray-Schauder不动点定理研究完全二阶非局部积分边值问题{-x″(t)=f(t,x(t),x′(t)),a.e.t∈[0,1],x(0)=∫10x(t)g(t)dt,x(1)=∫10x(t)h(t)dt解的存在性,唯一性以及解集的紧性,其中f:[0,1]×R^2→R为Carathéodory函数,g,h∈L^1[0,1]。

In this paper,by using Banach contraction mapping principle and Leray-Schauder fixed point theorem,for the following fully second-order nonloc boundary value problem {-x″（t）=f（t,x（t）,x′（t））, a.e.t∈[0,1],x（0）=∫10 x（t）g（t）dt, x（1）=∫10 x（t）h（t）dt we consider the compactness of solutions set,existence and uniqueness of solutions,where f：[0,1]×R2→Ris Carathéodory function,andg,h∈L1[0,1].