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陈瑞鹏 《西南大学学报(自然科学版)》2010,32(3)
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0ξ1ξ2…ξn…1. 相似文献
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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=1a_ix(ξ_i)解的存在性,其中f:[0,1]×R~2→R连续,e∈L~1[0,1],a_i∈R,ξ_i∈(0,1)(i=1,2,…) 满足0<ξ_1<ξ_2<…<ξ_n<…<1.Abstract: In this paper, we use the Leray-Schauder principle to study the existence of solutions of the infi-nite points boundary value problem of the second-order ordinary differential equation {x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1) x'(0)=0,x(1)=∞∑i=1a_ix(ξ_i)where f: [0,1]×R~2→R is continuous,e∈L~1[0,1],a_i∈R,ξ_i∈(0,1)(i=1,2,…)satisfy 0<ξ_1<ξ_2<…<ξ_n<…<1. 相似文献
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