About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 527082, 6 pages
http://dx.doi.org/10.1155/2013/527082
Research Article

Multiple Solutions for a Second-Order Impulsive Sturm-Liouville Equation

1College of Mathematics and Statistics, Jishou University, Jishou, Hunan 416000, China
2Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China

Received 29 March 2013; Revised 27 May 2013; Accepted 18 June 2013

Academic Editor: Gennaro Infante

Copyright © 2013 Jingli Xie and Zhiguo Luo. 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 solutions to a boundary value problem of a second-order impulsive Sturm-Liouville equation with a control parameter . By employing some existing critical point theorems, we find the range of the control parameter in which the boundary value problem admits at least three solutions. It is also shown that, under certain conditions, there exists an interval of the control parameter in which the boundary value problem possesses infinitely many solutions. Some examples are given to demonstrate the main results in this paper.