Multiple capture of the given number of evaders in the nonstationary example of L.S. Pontryagin

In the finite-dimensional Euclidean space, a generalized nonstationary example of L.S. Pontryagin with many participants is considered with the same dynamic and inertial capabilities of all players. The aim of the group of pursuers is to catch at least q evaders, and each evader must be caught by at least r pursuers. Assuming that evaders use program strategies, and each pursuer catches no more than one evader. Sufficient conditions for the solvability of the pursuit problem are obtained.