On impulsive semidynamical systems

It is now realized that the theory of impulsive differential equations is an important area of investigation. Moreover, the theory of such equations is much richer than the corresponding theory of differential equations [ 1, 21. In this paper we isolate the ideas involved in the theory of impulsive differential equations and initiate the study of impulsive semidynamical systems. For allied results on discontinuous dynamical systems see [3,4].