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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 717124, 13 pages
http://dx.doi.org/10.1155/2012/717124
Research Article

On Some Pursuit and Evasion Differential Game Problems for an Infinite Number of First-Order Differential Equations

1Department of Mathematics, Universiti Putra Malaysia, Serdang, 43400 Selangor, Malaysia
2Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, 43400 Selangor, Malaysia

Received 25 January 2012; Accepted 6 May 2012

Academic Editor: Debasish Roy

Copyright © 2012 Abbas Badakaya Ja'afaru and Gafurjan Ibragimov. 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 pursuit and evasion differential game problems described by infinite number of first-order differential equations with function coefficients in Hilbert space l2. Problems involving integral, geometric, and mix constraints to the control functions of the players are considered. In each case, we give sufficient conditions for completion of pursuit and for which evasion is possible. Consequently, strategy of the pursuer and control function of the evader are constructed in an explicit form for every problem considered.