Advances in Difference Equations
Volume 2007 (2007), Article ID 40160, 17 pages
doi:10.1155/2007/40160
Research Article

Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations

Y. Peng, X. Xiang, and W. Wei

Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China

Received 2 February 2007; Accepted 5 July 2007

Academic Editor: Paul W. Eloe

Copyright © 2007 Y. Peng 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 discuss the existence of optimal controls for a Lagrange problem of systems governed by the second-order nonlinear impulsive differential equations in infinite dimensional spaces. We apply a direct approach to derive the maximum principle for the problem at hand. An example is also presented to demonstrate the theory.