Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2024, Volume 231, Pages 3–12
DOI: https://doi.org/10.36535/2782-4438-2024-231-3-12 (Mi into1249) 		 
Periodic solutions of a differential equation with relay nonlinearity with delay

D. D. Bain

P.G. Demidov Yaroslavl State University
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DOI: https://doi.org/10.36535/2782-4438-2024-231-3-12
Abstract: For one class of second-order differential equations with relay nonlinearity and delay, orbitally stable periodic solutions are found by means of the recurrence operator, which is a suspension over some one-dimensional mapping. The analysis of this one-dimensional mapping shows that there exist domains of parameters for which exponentially orbitally stable periodic solutions exist.
Keywords: differential equation with delay, recurrence operator, stability
Funding agency Grant number
Russian Science Foundation 22-11-00209
This work was supported by the Russian Science Foundation (project No. 22-11-00209).
Document Type: Article
UDC: 517.929
MSC: 34K13, 34K39
Language: Russian
Citation: D. D. Bain, “Periodic solutions of a differential equation with relay nonlinearity with delay”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 231, VINITI, Moscow, 2024, 3–12
Citation in format AMSBIB
\Bibitem{Bai24}
\by D.~D.~Bain
\paper Periodic solutions of a differential equation with relay nonlinearity with delay
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 231
\pages 3--12
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1249}
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