一类二阶非线性方程三点边值问题解的存在性

Nontrivial Solution for A Second-Order Three-Point Boundary Value Problem

研究了一类二阶非线性常微分方程三点边值问题的非平凡解的存在性u″+f(t,u)=0,0≤t≤1,u′(0)=0,u(1)=αu(η);α∈R,0<η<1,f∈C([0,1]×R,R)。利用Leray-Schauder非线性诀择定理得到了非平凡解存在的一个充分条件,并给出一个实际例子的解法。

In this paper, a three-point boundary value problem for a second-order differential equation is investigated. By using Leray-Schauder nonlinear alternative, a sufficient condition for the existence of nontrivial solution is obtained with an example.