Periodic Solutions of Second Order Impulsive System for an Integro-Differential Equations with Maxima

A boundary value problem for a second order system of ordinary integro-differential equations with impulsive effects and maxima is investigated. Obtained a system of nonlinear functional integral equations. 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 is used in the proof of one-valued solvability of nonlinear functional integral equations. The questions of practical calculating of periodic solutions to given second order impulsive system of integro-differential equations are reduced to the calculations of nonzero index of the singular point of the integral mean.

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