najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-1-13-21najo-146Research ArticleMATHEMATICSМАТЕМАТИКАInverse problem for a second order impulsive system of integro-differential equations with two redefinition vectors and mixed maximaОбратная задача для импульсных систем интегро-дифференциальных уравнений второго порядка с двумя векторами переопределения и смешанными максимумамиhttps://orcid.org/0000-0002-9346-5362ЮлдашевТ. К.YuldashevT. K.

Турсун Камалдинович Юлдашев,

Ташкент.

T.K. Yuldashev,

49, Karimov street, Tashkent, 100066.

tursun.k.yuldashev@gmail.comhttps://orcid.org/0000-0001-6798-3265ФайзиевА. К.FayziyevA. K.

Азиз Кудратиллаевич  Файзиев,

Ташкент.

A.K. Fayziyev,

49, Karimov street, Tashkent, 100066.

fayziyev.a@inbox.ruTashkent State University of EconomicsUzbekistan2023050620251411321Copyright © Yuldashev T.K., Fayziyev A.K., 20252025Юлдашев Т.К., Файзиев А.К.Yuldashev T.K., Fayziyev A.K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/146

An inverse problem for a second order system of ordinary integro-differential equations with impulsive effects, mixed maxima and two redefinition vectors is investigated. A system of nonlinear functional integral equations is obtained by applying some transformations. The existence and uniqueness of the solution of the nonlinear inverse problem is reduced to the unique solvability of the system of nonlinear functional integral equations in Banach space PC ([0,T],Rn). The method of successive approximations in combination with the method of compressing mapping is used in the proof of unique solvability of the nonlinear functional integral equations. Then values of redefinition vectors are founded.

Исследуется обратная задача для системы обыкновенных интегро-дифференциальных уравнений второго порядка с импульсными воздействиями, смешанными максимумами и двумя векторами переопределения. Путем применения некоторых преобразований получается система нелинейных функциональных интегральных уравнений. Существование и единственность решения нелинейной обратной задачи сводится к однозначной разрешимости системы нелинейных функциональных интегральных уравнений в банаховом пространстве PC([0;T];Rn). Метод последовательных приближений в сочетании его с методом сжимающих отображений используется при доказательстве однозначной разрешимости нелинейных функциональных интегральных уравнений. Затем находятся значения векторов переопределения.

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The authors declare that there are no conflicts of interest present.