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.
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.