二阶m点边值问题的可解性  

Solvability of Second Order m-point Boundary Value Problem

作　　者：侯典国[1] 

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2008年第3期161-165,共5页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(10671169)

摘　　要：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.

关 键 词：边值问题 LERAY-SCHAUDER不动点定理 GREEN函数 

分 类 号：O175.8[理学—数学]