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

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

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.