Abstract and Applied Analysis
Volume 2012 (2012), Article ID 460171, 12 pages
http://dx.doi.org/10.1155/2012/460171
Research Article

A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints

Gafurjan Ibragimov1 and Nu'man Satimov2

1Institute for Mathematical Research and Department of Mathematics, Faculty of Science (FS), Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia
2Department of Mathematics, National University of Uzbekistan, Vuzgorodok, 100174 Tashkent, Uzbekistan

Received 5 July 2012; Revised 30 September 2012; Accepted 30 September 2012

Academic Editor: Jianquan Lu

Copyright © 2012 Gafurjan Ibragimov and Nu'man Satimov. 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 a simple motion pursuit differential game of many pursuers and many evaders on a nonempty convex subset of . In process of the game, all players must not leave the given set. Control functions of players are subjected to integral constraints. Pursuit is said to be completed if the position of each evader , , coincides with the position of a pursuer , , at some time , that is, . We show that if the total resource of the pursuers is greater than that of the evaders, then pursuit can be completed. Moreover, we construct strategies for the pursuers. According to these strategies, we define a finite number of time intervals and on each interval only one of the pursuers pursues an evader, and other pursuers do not move. We derive inequalities for the resources of these pursuer and evader and, moreover, show that the total resource of the pursuers remains greater than that of the evaders.