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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 1, Pages 38–56
DOI: https://doi.org/10.26907/0021-3446-2022-1-38-56 (Mi ivm9742) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Global stability of systems of nonlinear Itô differential equations with aftereffect and N.V. Azbelev's $W$-method

R. I. Kadievab, A. V. Ponosovc

a Daghestan Scientific Centre of Russian Academy of Sciences, M. Gadjieva str., 45, Makhachkala, 367032 Russia
b Dagestan State University, 43 a Hajiyev str., Makhachkala, 367000, Russia
c Norwegian University of Life Sciences, P.O. Box 5003 N-1432, As, Norway
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DOI: https://doi.org/10.26907/0021-3446-2022-1-38-56
Abstract: The work studies the global moment stability of solutions of systems of nonlinear differential Ito equations with delays. A modified regularization method ($W$ -method) for the analysis of various types of stability of such systems, based on the choice of the auxiliary equations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.
Keywords: nonlinear Itô equations, stability of solutions, method of auxiliary equations, positive invertibility of matrices, bounded delays.
Funding agency Grant number
Research Council of Norway 239070
Received: 30.03.2021
Revised: 19.04.2021
Accepted: 29.06.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 1, Pages 31–45
DOI: https://doi.org/10.3103/S1066369X22010030
Document Type: Article
UDC: 517.929:519.21
Language: Russian
Citation: R. I. Kadiev, A. V. Ponosov, “Global stability of systems of nonlinear Itô differential equations with aftereffect and N.V. Azbelev's $W$-method”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 1, 38–56; Russian Math. (Iz. VUZ), 66:1 (2022), 31–45
Citation in format AMSBIB
\Bibitem{KadPon22}
\by R.~I.~Kadiev, A.~V.~Ponosov
\paper Global stability of systems of nonlinear It\^{o} differential equations with aftereffect and N.V. Azbelev's $W$-method
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 1
\pages 38--56
\mathnet{http://mi.mathnet.ru/ivm9742}
\crossref{https://doi.org/10.26907/0021-3446-2022-1-38-56}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 1
\pages 31--45
\crossref{https://doi.org/10.3103/S1066369X22010030}
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    • This publication is cited in the following 1 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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