Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 490741, 14 pages
doi:10.1155/2010/490741
Research Article

Nonlinear Boundary Value Problem of First-Order Impulsive Functional Differential Equations

Kexue Zhang1 and Xinzhi Liu2

1School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
2Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Received 8 December 2009; Accepted 30 January 2010

Academic Editor: Shusen Ding

Copyright © 2010 Kexue Zhang and Xinzhi Liu. 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 investigates the nonlinear boundary value problem for a class of first-order impulsive functional differential equations. By establishing a comparison result and utilizing the method of upper and lower solutions, some criteria on the existence of extremal solutions as well as the unique solution are obtained. Examples are discussed to illustrate the validity of the obtained results.