一类二阶常微分方程边值问题解的存在性

Existence of Solutions of a Second Order Value Problem for Ordinary Differential Equation

设f:[0,1]×R2→R满足Caratheodory条件,a,b∈L1[0,1],a(.)≥0,b(t)≥0满足0≤∫01a(t)dt<1,0≤∫01b(t)dt<1,运用Leray-Schauder原理考虑了边值问题x″(t)=f(t,x(t),x′(t))+e(t),t∈[0,1],x′(0)=∫01b(t)x′(t)dt,x(1)=∫01a(t)x(t)dt解的存在性.

Let： f：[0,1]×R^2→R satisfies Carathodory condition,a,b∈L^1[0,1],a（·）≥0,b（t）≥0 and 0≤∫1 0 a（t）dt〈1,0≤∫1 0 b（t）dt〈1. By means of Leray-Sehauder Theorem the following problem is considered ：x″（t）=f（t,x（t）,x′（t））＋e（t）,t∈[0,1],x′（0）=∫1 0b（t）x′（t）dt,x（1）=∫1 0 a（t）x（t）dtThe criteria of admitting solutions for boundary value problem of second order ordinary differential equation is established.