Problem of multiple capture of given number of evaders in recurrent differential games

The problem of pursuit by a group of pursuers of a group of evaders with equal opportunities for all participants and geometric restrictions on the control of players is considered. The evaders use program strategies, each pursuer catches no more than one evader. The goal of the pursuers is to catch a given number of evaders, and each evader needs to be caught no less than a certain number of pursuers. In this paper, sufficient conditions are obtained for multiple capture of a given number of evaders.