International Journal of Pure and Applied Mathematics Volume 114 No. 4 2017, 759-770 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v114i4.6 P A ijpam.eu EVASION DIFFERENTIAL GAME OF TWO PURSUERS AND ONE EVADER WITH COORDINATE-WISE INTEGRAL CONSTRAINTS Piriatharisini Karapanan 1 § , Gafurjan Ibragimov 2 , Idham Arif Alias 3 1 Institute for Mathematical Research Universiti Putra Malaysia 43400 UPM Serdang, Selangor, MALAYSIA 2,3 Institute for Mathematical Research and Department of Mathematics Faculty of Science Universiti Putra Malaysia 43400 UPM Serdang, Selangor, MALAYSIA Abstract: An evasion differential game of two pursuers and one evader in R 2 is studied. Un- like the traditional integral constraints, in the present work, integral constraints are imposed on each component of control functions of the players. By definition, evasion is said to be pos- sible if the state of a pursuer does not coincide with that of the evader for all t ≥ 0. Sufficient conditions of evasion are obtained and then strategies for the evader are constructed. AMS Subject Classification: 91A23, 49N75 Key Words: control, coordinate-wise integral constraint, differential game, evasion, strategy 1. Introduction A number of studies were carried out for differential games (see, e.g., [7]–[9]) and differential games with integral constraints were studied in many papers (see, e.g., [1], [3], [10]) but there are only a few papers for evasion differential games from many pursuers with integral constraints. Received: October 9, 2016 Revised: April 7, 2017 Published: June 7, 2017 c  2017 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author