Periodic solutions for an impulsive system of integro-differential equations with maxima

A periodical boundary value problem for a first-order system of ordinary integro-differential equations with impulsive effects and maxima is investigated. A system of nonlinear functional-integral equations is obtained and the existence and uniqueness of the solution of the periodic boundary value problem are reduced to the solvability of the system of nonlinear functional-integral equations. The method of successive approximations in combination with the method of compressing mapping is used in the proof of one-valued solvability of nonlinear functional-integral equations. We define the way with the aid of which we could prove the existence of periodic solutions of the given periodical boundary value problem.