Advances in Difference Equations
Volume 2009 (2009), Article ID 848191, 19 pages
doi:10.1155/2009/848191
Research Article

Existence of Positive Solutions in Generalized Boundary Value Problem for p-Laplacian Dynamic Equations on Time Scales

Wenyong Zhong1,2 and Wei Lin1

1Research Center and Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
2School of Mathematics and Computer Sciences, Jishou University, Hunan 416000, China

Received 31 March 2009; Accepted 7 May 2009

Academic Editor: Alberto Cabada

Copyright © 2009 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

We analytically establish the conditions for the existence of at least two or three positive solutions in the generalized m-point boundary value problem for the p-Laplacian dynamic equations on time scales by means of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem. Furthermore, we illustrate the possible application of our analytical results with a concrete and nontrivial dynamic equation on specific time scales.