Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 111, pp. 1-10

Title: Nontrivial solution for a three-point boundary-value problem

Author: Yong-Ping Sun (Hangzhou Radio and TV Univ., China)

Abstract: 
 In this paper, we study the existence of nontrivial
 solutions for the second-order three-point boundary-value problem
 $$\displaylines{
 u''+f(t,u)=0,\quad  0<t<1, \cr
 u'(0)=0,\quad u(1)=\alpha u'(\eta).
 }$$
 where $\eta \in (0,1)$, $\alpha \in \mathbb{R}$,
 $f\in C([0,1]\times \mathbb{R},\mathbb{R})$.
 Under certain growth conditions on the nonlinearity  $f$
 and by using  Leray-Schauder nonlinear alternative,
 sufficient conditions for the existence of nontrivial solution
 are obtained. We illustrate the results obtained with some examples.
 
Submitted June 15, 2004. Published September 22, 2004.
Math Subject Classifications: 34B10, 34B15.
Key Words: Three-point boundary-value problem; nontrivial solution;
           Leray-Schauder nonlinear alternative.