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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 572172, 11 pages
http://dx.doi.org/10.1155/2012/572172
Research Article

Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space

1School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
2School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
3Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia

Received 20 February 2012; Accepted 13 June 2012

Academic Editor: Shaoyong Lai

Copyright © 2012 Hua Su 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

We consider the existence of single and multiple positive solutions for a second-order Sturm-Liouville boundary value problem in a Banach space. The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. Our results significantly extend and improve many known results including singular and nonsingular cases.