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Abstract and Applied Analysis
Volume 2012, Article ID 707163, 19 pages
http://dx.doi.org/10.1155/2012/707163
Research Article

Existence of Solutions for Sturm-Liouville Boundary Value Problem of Impulsive Differential Equations

1School of Mathematics and Statistics, Lanzhou University, Gansu, Lanzhou 730000, China
2Departamento de Análisis Matemático, Universidad de Santiago de Compostela, Santiago de Compostela 15782, Spain
3Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 20 January 2012; Revised 13 March 2012; Accepted 3 April 2012

Academic Editor: D. O'Regan

Copyright © 2012 Hong-Rui Sun 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

This paper is concerned with the existence of solutions for Sturm-Liouville boundary value problem of a class of second-order impulsive differential equations, under different assumptions on the nonlinearity and impulsive functions, existence criteria of single and multiple solutions are established. The main tools are variational method and critical point theorems. Some examples are also given to illustrate the main results.