Advances in Difference Equations
Volume 2009 (2009), Article ID 737461, 14 pages
doi:10.1155/2009/737461
Necessary and sufficient conditions for the existence of positive solution for singular boundary value problems on time scales
Meiqiang Feng1
, Xuemei Zhang2
, Xianggui Li1
and Weigao Ge4
1School of Science, Beijing Information Science \& Technology University, Beijing 100192, China
2Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
4Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China
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.