Open Access Research Article

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

Kexue Zhang1 and Xinzhi Liu2*

Author Affiliations

1 School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China

2 Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

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Journal of Inequalities and Applications 2010, 2010:490741  doi:10.1155/2010/490741

Published: 21 February 2010

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.