Abstract
In the Hilbert space l2, we investigate a pursuit-evasion differential game involving countable number of pursuers and one evader. Players move in agreement with certain nth order ordinary differential equations with control functions of players satisfying integral constraints. The period of the game, which is denoted as θ, is fixed. During the game, pursuers want to minimize the distance to the evader and the evader want to maximize it. The game's payoff is the distance between evader and closest pursuer at time θ. Independent of relationship between energy resources of the players, we provide formula that defines value of the game and constructed players' optimal strategies.
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