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.
出处
《烟台大学学报(自然科学与工程版)》
CAS
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)