二阶m点边值问题的可解性

Solvability of Second Order m-point Boundary Value Problem

设f:[0,1]×R2→R满足Caratheodory条件,(1-t)e(t)∈L1[0,1],0<ξ1<ξ2<…<ξm-2<1.本文运用Leray-Schauder不动点定理来考虑m点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1),α0x(0)+α1x'(0)=0,x(1)=∑m-2i=1βix(ξi),C[0,1]∩C1[0,1)解的存在性.

Letting f：[0,1]×R^2→R be a function satisfying Caratheodory condition,1-t）e（t）∈L^1[0,1],0〈ξ1〈ξ2〈…ξm-2〈1we discuss the problem of existence of a C[0,1]∩C^1[0,1）solution forthe m-point boundary value problem x″（t）=f（t,x（t）,x（t））,＋e（t）,t∈（0,1）,α0x（0）＋α1x（0）=0,x（1）=∑i=1^m-2βix（ξi）,The proof of main result is based upon the Leray-Schauder fixed theorem.