International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 513189, 7 pages
http://dx.doi.org/10.1155/2012/513189
Research Article

On a Third-Order Three-Point Boundary Value Problem

A. Guezane-Lakoud,1 N. Hamidane,1 and R. Khaldi2

1Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria
2Laboratory LASEA, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria

Received 28 March 2012; Accepted 3 June 2012

Academic Editor: Rodica Costin

Copyright © 2012 A. Guezane-Lakoud et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a third-order three-point boundary value problem. We introduce a generalized polynomial growth condition to obtain the existence of a nontrivial solution by using Leray-Schauder nonlinear alternative, then we give an example to illustrate our results.