摘要
运用Leray-Schauder原理考察了二阶常微分方程边值问题x″(t)=f(t,x(t),x′(t))+e(t),t∈(0,1)x′(0)=0,x(1)=∑∞i=1aix(ξi)解的存在性,其中f:[0,1]×R2R连续,e∈L1[0,1],ai∈R,ξi∈(0,1)(i=1,2,…)满足0<ξ1<ξ2<…<ξn<…<1.
In this paper, we use the Leray-Schauder principle to study the existence of solutions of the infinite points boundary value problem of the second order ordinary differential equation { x″(t)=f(t,x(t)+e(t),t∈(0,1) x′(0)=0〈,x(1)=∑i=1^∞aix(ξi) where f:[0,1]×R^2→R is continuous,e∈L^1[0,1],ai∈R,ξi∈(0,1)(i=1,2,…) satisfy 0〈ξ1〈ξ2〈…〈ξn〈…〈1.
出处
《西南大学学报(自然科学版)》
CAS
CSCD
北大核心
2010年第3期25-29,共5页
Journal of Southwest University(Natural Science Edition)
基金
国家自然科学基金资助项目(10671158)
甘肃省自然科学基金资助项目(3ZS051-A25-016)