Copyright © 2009 Yanbin Sang. 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 higher-order three-point boundary value problem on time scales. A new existence result is first obtained by using a fixed point theorem due to Krasnoselskii and Zabreiko. Later, under certain growth conditions imposed on the nonlinearity, several sufficient conditions for the existence of a nonnegative and nontrivial solution are obtained by using Leray-Schauder nonlinear alternative. Our conditions imposed on nonlinearity are all very easy to verify; as an application, some examples to demonstrate our results are given.