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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 168, Pages 91–98 (Mi into504)  

Stability and asymptotically periodic solutions of hybrid systems with aftereffect

P. M. Simonov

Perm State National Research University

Abstract: In this paper, we study hybrid linear systems of functional differential equations with aftereffect using the Azbelev $W$-method. Two model equations are considered and Banach spaces of right-hand sides and solutions, which are spaces of asymptotically periodic functions, are examined. Analogs of the Bohl–Perron theorem on the asymptotic stability and on the existence of limits of solutions are obtained.

Keywords: Bohl–Perron theorem, asymptotically periodic functions, hybrid system, functional differential equation, equation with aftereffect, stability, method of model equations

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00332-а
This work was supported by the Russian Foundation for Basic Research (project No. 18-01-00332-a).


DOI: https://doi.org/10.36535/0233-6723-2019-168-91-98

Full text: PDF file (205 kB)
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UDC: 517.977
MSC: 34K20, 34K25

Citation: P. M. Simonov, “Stability and asymptotically periodic solutions of hybrid systems with aftereffect”, Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 168, VINITI, Moscow, 2019, 91–98

Citation in format AMSBIB
\Bibitem{Sim19}
\by P.~M.~Simonov
\paper Stability and asymptotically periodic solutions of hybrid systems with aftereffect
\inbook Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25--28, 2018. Part 1
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 168
\pages 91--98
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into504}
\crossref{https://doi.org/10.36535/0233-6723-2019-168-91-98}


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