Periodic solutions of nonlinear impulsive differential inclusions with constraints

In this paper we obtain the existence of periodic solutions for nonlinear invariance problems monitored by impulsive differential inclusions subject to impulse effects. In our proof we use the result due to Hristova and Bainov concerning the existence of a periodic solution for impulsive differential equations, together with an approximation argument. Our Theorems 3.1 and 3.2 extend the existence result proved by Watson (see Remarks 3.1 and 3.2) and, moreover, improve the Hristova - Bainov existence theorem in the case of "invariance" problems involving impulsive differential equations.