Advances in Difference Equations
Volume 2010 (2010), Article ID 746106, 20 pages
doi:10.1155/2010/746106
Research Article

Time-Scale-Dependent Criteria for the Existence of Positive Solutions to p-Laplacian Multipoint Boundary Value Problem

Wenyong Zhong1 and Wei Lin2

1School of Mathematics and Computer Sciences, Jishou University, Hunan 416000, China
2Shanghai Key Laboratory of Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received 1 May 2010; Revised 23 July 2010; Accepted 30 July 2010

Academic Editor: Alberto Cabada

Copyright © 2010 Wenyong Zhong and Wei Lin. 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

By virtue of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem, we analytically establish several sufficient criteria for the existence of at least two or three positive solutions in the p-Laplacian dynamic equations on time scales with a particular kind of p-Laplacian and m-point boundary value condition. It is this kind of boundary value condition that leads the established criteria to be dependent on the time scales. Also we provide a representative and nontrivial example to illustrate a possible application of the analytical results established. We believe that the established analytical results and the example together guarantee the reliability of numerical computation of those p-Laplacian and m-point boundary value problems on time scales.