一类奇异非线性二阶边值问题解的存在性

Solvability of a Singular Nonlinear Second Order Boundary Value Problems

设f:[0,1]×R2→R满足Caratheodory条件,a∈L1[0,1]且1∫0a(t)dt≠0,(1-t)e(t)∈L1(0,1).运用Leray-Schauder原理考虑了二阶奇异边值问题:x″(t)=f(t,x(t),x(′t))+e(t),t∈(0,1)x′(0)=0,x(1)=1∫0a(t)x(t)dt,在C1[0,1)上解的存在性.

Let f1[0,1]×R^2→R be a function satisfying Caratheodory＇ s conditions and （1-t）e（t）∈L^1（0,1） ,and let∫10a（t）dt≠0,（1-t）e（t）∈L^1（0,1） be given. The problem of existence of a C^1[0,1） solution for the m-point boundary value problem is concerned with based upon the Leray, Sehauder continuation theorem {x″（t）=f（t,x（t）,x′（t））＋e（t）,t∈（0,1）;x′（0）=1,x（1）=∫10a（t）x（t）dt,