On pursuit-evasion differential game problem in a Hilbert space

We consider a pursuit-evasion differential game problem in which countably many pursuers chase one evader in the Hilbert space l(2) and for a fixed period of time. Dynamic of each of the pursuer is governed by first order differential equations and that of the evader by a second order differential equation. The control function for each of the player satisfies an integral constraint. The distance between the evader and the closest pursuer at the stoppage time of the game is the payoff of the game. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. We constructed optimal strategies of the players and find value of the game.