非线性增长条件下一类非线性无穷多点边值问题的可解性

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~10,1],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~10,1],a_i∈R,ξ_i∈(0,1)(i=1,2,…)satisfy 0＜ξ_1＜ξ_2＜…＜ξ_n＜…＜1.

Solvability of a Nonlinear Infinite Points Boundary Value Problem with Nonlinear Growth