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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 6, Pages 25–36 (Mi ivm8802)  
This article is cited in 6 scientific papers (total in 6 papers)

Stability of solutions to differential equations with several variable delays. I

V. V. Malygina, K. M. Chudinov

Chair of Computational Mathematics and Mechanics, State National Research Polytechnical University of Perm, Perm, Russia
Full-text PDF (236 kB) Citations (6)
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Abstract: We consider a class of scalar linear differential equations with several variable delays and constant coefficients. A family of equations of the class is defined by coefficients and maximum admissible values of delays. We obtain conditions that are necessary and sufficient for the stability of solutions to all equations of the family. It is ascertained that the conditions are determined entirely by properties of the solution to the initial problem for an autonomous equation that belongs to the family. Some alternatives of required conditions are obtained in the form of estimates for solutions to autonomous equations in a finite interval.
Keywords: functional differential equation, varying delay, several delays, stability, the Cauchy function.
Received: 27.03.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 6, Pages 21–31
DOI: https://doi.org/10.3103/S1066369X13060030
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: V. V. Malygina, K. M. Chudinov, “Stability of solutions to differential equations with several variable delays. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 6, 25–36; Russian Math. (Iz. VUZ), 57:6 (2013), 21–31
Citation in format AMSBIB
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\paper Stability of solutions to differential equations with several variable delays.~I
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 6
\pages 25--36
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 6
\pages 21--31
\crossref{https://doi.org/10.3103/S1066369X13060030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878781566}
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    This publication is cited in the following 6 articles:
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