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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 7, Pages 29–38 (Mi ivm1637)  
This article is cited in 5 scientific papers (total in 5 papers)

On the problem of the stability of functional-differential equations with infinite delay

S. V. Pavlikov

Kama State Engineering-Economics Academy, Naberezhnye Chelny, Russia
Full-text PDF (205 kB) Citations (5)
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Abstract: We study the stability of functional differential equations with infinite delay, using the Lyapunov functional of constant sign with a derivative of constant sign. Limit equations are constructed in a special phase space. We establish a theorem on localization of a positive limit set and theorems on the stability and the asymptotic stability. The results are illustrated by examples.
Keywords: functional differential equation, infinite delay, Lyapunov functional of constant sign, limit equations.
Received: 23.05.2006
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 7, Pages 24–32
DOI: https://doi.org/10.3103/S1066369X08070049
Bibliographic databases:
UDC: 517.929
Language: Russian
Citation: S. V. Pavlikov, “On the problem of the stability of functional-differential equations with infinite delay”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 7, 29–38; Russian Math. (Iz. VUZ), 52:7 (2008), 24–32
Citation in format AMSBIB
\Bibitem{Pav08}
\by S.~V.~Pavlikov
\paper On the problem of the stability of functional-differential equations with infinite delay
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 7
\pages 29--38
\mathnet{http://mi.mathnet.ru/ivm1637}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2467443}
\zmath{https://zbmath.org/?q=an:1189.34146}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 7
\pages 24--32
\crossref{https://doi.org/10.3103/S1066369X08070049}
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  • https://www.mathnet.ru/eng/ivm1637
  • https://www.mathnet.ru/eng/ivm/y2008/i7/p29
    • This publication is cited in the following 5 articles:
    1. A. S. Andreev, O. A. Peregudova, “On the Stability and Stabilization Problems of Volterra Integro-Differential Equations”, Nelin. Dinam., 14:3 (2018), 387–407  mathnet  crossref  elib
    2. Pham Huu Anh Ngoc, Cao Thanh Tinh, “Explicit Criteria For Exponential Stability of Time-Varying Systems With Infinite Delay”, Math. Control Signal Syst., 28:1 (2016), 4  crossref  mathscinet  zmath  isi
    3. Pavlikov S.V., Rastorguev D.N., “Ob ustoichivosti modelei regionalnykh sotsialno-ekonomicheskikh sistem s uchetom investitsionnykh vlozhenii”, V mire nauchnykh otkrytii, 2012, 232–250  elib
    4. A. S. Andreev, “The Lyapunov functionals method in stability problems for functional differential equations”, Autom. Remote Control, 70:9 (2009), 1438–1486  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Sedova N.O., “Stability in systems with unbounded aftereffect”, Autom. Remote Control, 70:9 (2009), 1553–1564  mathnet  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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