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Journal of Applied Mathematics
Volume 2014, Article ID 575204, 12 pages
http://dx.doi.org/10.1155/2014/575204
Research Article

Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations

1Department of Applied Mathematics, Jilin University of Finance and Economics, Changchun, Jilin 130117, China
2School of Mathematics and Computer, Harbin University, Harbin 150086, China

Received 2 June 2014; Accepted 21 July 2014; Published 17 August 2014

Academic Editor: Daqing Jiang

Copyright © 2014 Zhongwei Cao 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 study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007) . In some suitable weak singularities, the existence of periodic solutions may help.