Abstract:
A periodical boundary value problem for a first-order system of ordinary integro-differential equations with impulsive effects and maxima is investigated. A system of nonlinear functional-integral equations is obtained 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.
Keywords:
impulsive integro-differential equations, periodical boundary value condition, nonlinear kernel, compressing mapping, existence and uniqueness of periodic solution.
Citation:
T. K. Yuldashev, “Periodic solutions for an impulsive system of integro-differential equations with maxima”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:2 (2022), 368–379
\Bibitem{Yul22}
\by T.~K.~Yuldashev
\paper Periodic solutions for an impulsive system of~integro-differential equations with maxima
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2022
\vol 26
\issue 2
\pages 368--379
\mathnet{http://mi.mathnet.ru/vsgtu1917}
\crossref{https://doi.org/10.14498/vsgtu1917}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4450725}
\edn{https://elibrary.ru/TYZLDB}
Linking options:
https://www.mathnet.ru/eng/vsgtu1917
https://www.mathnet.ru/eng/vsgtu/v226/i2/p368
This publication is cited in the following 2 articles:
M. P. Eshov, N. N. Kodirov, T. K. Yuldashev, “Zadachi optimizatsii v obyknovennykh avtonomnykh sistemakh pervogo poryadka”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 227, VINITI RAN, M., 2023, 92–99
Aziz Fayziyev, “NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM FOR A SECOND ORDER IMPULSIVE SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS WITH MIXED MAXIMA”, VOGUMFT, 2023, no. 2(3), 208
Citation in format AMSBIB
Contact us: