Abstract and Applied Analysis
Volume 2012 (2012), Article ID 903281, 20 pages
http://dx.doi.org/10.1155/2012/903281
Research Article

Subharmonic Solutions of Nonautonomous Second Order Differential Equations with Singular Nonlinearities

N. Daoudi-Merzagui,1 F. Derrab,2 and A. Boucherif3

1Department of Mathematics, University of Tlemcen, Tlemcen 13000, Algeria
2Department of Mathematics, University of Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria
3Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhahran 31261, Saudi Arabia

Received 4 November 2011; Revised 14 January 2012; Accepted 19 January 2012

Academic Editor: Juan J. Nieto

Copyright © 2012 N. Daoudi-Merzagui 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 discuss the existence of subharmonic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions are provided enable us to obtain infinitely many distinct subharmonic solutions. Our approach is based on a variational method, in particular the saddle point theorem.