On a Multiperson Pursuit Problem with Integral Constraints on the Controls of the Players

We consider a linear multiperson differential game with integral constraints on the control of the players. The pursuit is assumed terminated if the solution of at least one of the equations describing the game reaches the origin at some instant of time. In the case of one pursuer, we obtain a necessary and sufficient condition for terminating pursuit from all points of space. In the case of many pursuers, we obtain a sufficient condition for terminating pursuit from all points of space.