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In this paper, we study a pursuit-evasion differential game problem in the Hilbert spaceDynamics of countable number of pursuers and evader expressed as  n th-order differential equations with geometric constraints on the control functions of the players. The game terminates at a given fixed time which is denoted by  ϑ . The game's payoff is the infimum of the distances between the evader and pursuers at the time  ϑ . According to the rule of the game, pursuers try to minimise the distance to the evader and the evader tries to maximises it. We found value of the game and constructed players' optimal strategies.

A game problem of pursuit-evasion with n th order differential equations describing players' dynamics