Abstract and Applied Analysis
Volume 2013 (2013), Article ID 134691, 9 pages
http://dx.doi.org/10.1155/2013/134691
Research Article

Existence Result for Impulsive Differential Equations with Integral Boundary Conditions

Peipei Ning, Qian Huan, and Wei Ding

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received 5 December 2012; Accepted 5 January 2013

Academic Editor: Yonghui Xia

Copyright © 2013 Peipei Ning 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 investigate the following differential equations: , with impulsive and integral boundary conditions , , , , where . The expression of Green's function and the existence of positive solution for the system are obtained. Upper and lower bounds for positive solutions are also given. When , , , and take different values, the system can be simplified to some forms which has been studied in the works by Guo and LakshmiKantham (1988), Guo et al. (1995), Boucherif (2009), He et al. (2011), and Atici and Guseinov (2001). Our discussion is based on the fixed point index theory in cones.