Advances in Difference Equations
Volume 2009 (2009), Article ID 219251, 14 pages
doi:10.1155/2009/219251
Research Article

Multiple Positive Solutions for a Class of m-Point Boundary Value Problems on Time Scales

Meiqiang Feng,1 Xuemei Zhang,2,3 and Weigao Ge3

1School of Science, Beijing Information Science & Technology University, Beijing 100192, China
2Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
3Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 1 December 2008; Revised 15 April 2009; Accepted 10 June 2009

Academic Editor: Victoria Otero-Espinar

Copyright © 2009 Meiqiang Feng 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.

Abstract

By constructing an available integral operator and combining Krasnosel'skii-Zabreiko fixed point theorem with properties of Green's function, this paper shows the existence of multiple positive solutions for a class of m-point second-order Sturm-Liouville-like boundary value problems on time scales with polynomial nonlinearity. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example, which cannot be handled using the existing results.