Advances in Difference Equations
Volume 2009 (2009), Article ID 737461, 14 pages
doi:10.1155/2009/737461
Research Article

Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

Meiqiang Feng,1 Xuemei Zhang,2,3 Xianggui Li,1 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 27 March 2009; Revised 3 July 2009; Accepted 15 September 2009

Academic Editor: Alberto Cabada

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 available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of Cld[0,1]𝕋 as well as CldΔ[0,1]𝕋 positive solutions for a class of singular boundary value problems on time scales. 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.