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

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Abstract

A periodical boundary value problem for a first-order system of ordinary integro-differential equations with impulsive effects and maxima is investigated. The obtained system of nonlinear functional-integral equations 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.

About the authors

Tursun K. Yuldashev

National University of Uzbekistan named after Mirzo Ulugbek

Author for correspondence.
Email: tursun.k.yuldashev@gmail.com
ORCID iD: 0000-0002-9346-5362
SPIN-code: 1629-8554
Scopus Author ID: 24482650300
http://www.mathnet.ru/person27151

Dr. Phys. & Math. Sci., Professor, Uzbek-Israel Joint Faculty

Uzbekistan, 4, Vuzgorodok, Universitetskaya st., Tashkent, 100174

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