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Nanosystems: Phys. Chem. Math., 2022, 13 (1), 36–44

On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima

Tursun K. Yuldashev – National University of Uzbekistan, Tashkent, Uzbekistan; atursun.k.yuldashev@gmail.com
Aziz K. Fayziev – Tashkent State Technical University, Tashkent, Uzbekistan; bfayziyev.a@inbox.ru

Corresponding author: Tursun K. Yuldashev, tursun.k.yuldashev@gmail.com

DOI 10.17586/2220-8054-2022-13-1-36-44

ABSTRACT A nonlocal boundary value problem for a system of ordinary integro-differential equations with impulsive effects, degenerate kernel and maxima is investigated. The boundary value problem is given by the integral condition. The method of successive approximations in combination 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 solution on the right-hand side of the boundary value condition is shown.

KEYWORDS impulsive integro-differential equations, nonlocal condition, successive approximations, existence and uniqueness, continuous dependence of solution

FOR CITATION Yuldashev T.K., Fayziev A.K. On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima. Nanosystems: Phys. Chem. Math., 2022, 13 (1), 36–44.

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