一类二阶奇异边值问题解的存在性

Existence of solutions to a category of singular second-order boundary-value problems

设f:[0,1]×R2→R满足Caratheodory条件(1-t)e(t)∈L1(0,1),∫01a(t)tdt≠1,a(t)t∈L1[0,1].运用Leray-Schauder原理考虑二阶奇异边值问题x″(t)=f(t,x(t),x′(t))+e(t),0<t<1;x(0)=0,x(1)=∫01a(t)x(t)dt在C1[0,1)上解的存在性.

Let f：[0,1]×R2→Rbe a function meeting Caratheodory＇s conditions, （1-t）e（t）∈L^1 （0, 1）, and ∫0^1a（t）tdt≠1,a（t）t∈L1[0,1]. The existence of solutions to the singular second-order boundary-value floa（t）x（t）dt on problemx″（t）=f（t,x（t）,x′（t））＋e（t）,0〈t〈1;x（0）=0,x（1）= ∫0^1a（t）x（t）dt on C^1[0,1] was taken into consideration by using Leray-Schauder principle.