Electron. J. Diff. Eqns., Vol. 2004(2004), No. 111, pp. 1-10

Nontrivial solution for a three-point boundary-value problem

Yong-Ping Sun

Abstract:
In this paper, we study the existence of nontrivial solutions for the second-order three-point boundary-value problem
$$\displaylines{ u''+f(t,u)=0,\quad 0 less than t less than 1, \cr u'(0)=0,\quad u(1)=\alpha u'(\eta). }$$
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.

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Yong-Ping Sun
Department of Fundamental Courses
Hangzhou Radio and TV University
Hangzhou, Zhejiang 310012, China
email: syp@mail.hzrtvu.edu.cn

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