Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 903653, 13 pages
Research Article

Existence of Periodic Solutions for the Duffing Equation with Impulses

1Department of Mathematics, Hunan First Normal University, Hunan, Changsha 410205, China
2Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsinki, Finland
3Department of Mathematics, Hunan University of Science and Technology, Hunan, Xiangtan 411201, China
4Department of Mathematics, Hangzhou Normal University, Zhejiang, Hangzhou 310036, China

Received 3 November 2011; Revised 10 December 2011; Accepted 22 January 2012

Academic Editor: F. Lobo Pereira

Copyright © 2012 Xuxin Yang 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.


We study the existence of solutions to the Duffing equation with impulses. By means of the Poincaré-Birkhoff fixed point theorem under given conditions, we obtain the sufficient condition of existence of infinitely many solutions. Our results generalize those of T. R. Ding. An example is presented to demonstrate applications of our main result.