Complete solution of a class of differential pursuit games with integral constraint and impulse control

In this paper, we consider one class of differential games, for which, using the method of resolving functions, we have finally solved the problem of the possibility or impossibility of catching the evader from a given initial point by the pursuer. In this case, an integral constraint is imposed on the controls of the pursuer, and the control of the evader has an impulsive character, and it is represented using a generalized Dirac function.