一类二阶常微分方程泛函边值问题解的存在性

Existence of solutions for a functional boundary value problem of second order ordinary differential equations

运用打靶法考虑了二阶常微分方程泛函边值问题x″(t)=f(t,x(t),x′(t)),t∈[0,1],x(0)=0,x(1)=∫01a(t)x(t)dt解的存在性,给出了此类问题解的存在性判据,其中f:[0,1]×R2→R满足Carathéodory条件,a∈C([0,1],[0,∞)),且∫01a(t)tdt<1.

By using the shooting method, the existence of solutions of the following functional boundary value problem {x″（t）=f（t,x（t）,x′（t））,t∈[0,1],x（0）=0,x（1）=∫0^1α（t）x（t）dt are obtained, where f：[0,1]×R^2→R satisfy Carathéodory condition α∈C（[0,1],[0,∞）） , and ∫0^1α（t）tdt〈1.