Existence and Multiplicity of Solutions to a Boundary Value Problem for Impulsive Differential Equations

Chunyan He, Yongzhi Liao, and Yongkun Li 1 Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China 2 School of Mathematics and Computer Science, Panzhihua University, Panzhihua, Sichuan 617000, China Correspondence should be addressed to Yongkun Li; [email protected] Received 24 October 2012; Revised 20 December 2012; Accepted 21 December 2012 Academic Editor: Wan-Tong Li Copyright © 2013 Chunyan He 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 investigate the existence and multiplicity of solutions to a boundary value problem for impulsive differential equations. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, at least two solutions, and infinitely many solutions. Some examples are given to illustrate the effectiveness of our results.