Vestnik КRAUNC. Fiz.-Mat. nauki. 2022. vol. 38. no. 1. P. 40-53. ISSN 2079-6641

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MSC 34B37, 34B15

Research Article

On a nonlocal problem for impulsive differential equations with mixed maxima

T. K. Yuldashev¹²

¹National University of Uzbekistan, 100174, Tashkent, Universitetskaya street, 4, Uzbekistan
²V. I. Romanovskii Institute of Mathematics, Academy of Sciences of Uzbekistan, 100174, Tashkent, Universitetskaya street, 4-B, Uzbekistan

E-mail: tursun.k.yuldashev@gmail.com

A nonlocal boundary value problem for a first order system of ordinary integro-differential equations with impulsive effects and mixed maxima is investigated. The boundary value problem is given by the integral condition. The method of successive approximations in combination it with the method of compressing mapping is used. The existence and uniqueness of the solution of the boundary value problem are proved. The continuous dependence of the solutions on the right-hand side of the boundary condition is showed.

Key words: impulsive integro-differential equations, nonlocal boundary condition, mixed maxima, successive approximations, existence and uniqueness of solution, continuous dependence of solution.

DOI: 10.26117/2079-6641-2022-38-1-40-53

Original article submitted: 02.03.2022

Revision submitted: 21.04.2022

For citation. Yuldashev T. K. On a nonlocal problem for impulsive differential equations with mixed maxima. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 38: 1, 40-53. DOI: 10.26117/2079-6641-2022-38-1-40-53

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Yuldashev T. K., 2022

Competing interests. The author declares that there are no conflicts of interest with respect to authorship and publication.

Contribution and responsibility. The author contributed to the writing of the article and is solely responsible for submitting the final version of the article to the press. The final version of the manuscript was approved by the author.

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Yuldashev Tursun Kamaldinovich – D. Sci. (Phys. & Math.), Associate Professor, Professor of the Uzbek-Israel Joint Fac., National University of Uzbekistan, Tashkent, Uzbekistan, ORCID 0000-0002-9346-5362.

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