Abstract and Applied Analysis
Volume 2009 (2009), Article ID 341679, 16 pages
doi:10.1155/2009/341679

Solvability of a higher-order three-point boundary value problem on time scales

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.