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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2010, Volume 10, Issue 3, Pages 17–29 (Mi vngu47)  

This article is cited in 10 scientific papers (total in 10 papers)

Stability of solutions to differential equations of neutral type

G. V. Demidenkoab, T. V. Kotovab, M. A. Skvortsovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
References:
Abstract: In the present paper we study stability of solutions to systems of quasi-linear delay differential equations of neutral type
ddt(y(t)+Dy(tτ))=Ay(t)+By(tτ)+F(t,y(t),y(tτ)),t>τ,
where A, B, D are n×n numerical matrices, τ>0 is a delay parameter, F(t,u,v) is a real-valued vector-function satisfying Lipschitz condition with respect to u and F(t,0,0)=0. Stability conditions of the zero solution to the systems are obtained, uniform estimates for the solutions on the half-axis {t>τ} are established. In the case of asymptotic stability these estimates give the decay rate of the solutions at infinity.
Keywords: quasi-linear differential equations of neutral type, asymptotic stability, attraction domain, uniform estimates for solutions, modified Lyapunov–Krasovskii functional.
Received: 30.06.2009
English version:
Journal of Mathematical Sciences, 2012, Volume 186, Issue 3, Pages 394–406
DOI: https://doi.org/10.1007/s10958-012-0994-x
Document Type: Article
UDC: 517.929.4
Language: Russian
Citation: G. V. Demidenko, T. V. Kotova, M. A. Skvortsova, “Stability of solutions to differential equations of neutral type”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 10:3 (2010), 17–29; J. Math. Sci., 186:3 (2012), 394–406
Citation in format AMSBIB
\Bibitem{DemKotSkv10}
\by G.~V.~Demidenko, T.~V.~Kotova, M.~A.~Skvortsova
\paper Stability of solutions to differential equations of neutral type
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2010
\vol 10
\issue 3
\pages 17--29
\mathnet{http://mi.mathnet.ru/vngu47}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 186
\issue 3
\pages 394--406
\crossref{https://doi.org/10.1007/s10958-012-0994-x}
Linking options:
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  • https://www.mathnet.ru/eng/vngu/v10/i3/p17
  • This publication is cited in the following 10 articles:
    1. Yener Altun, “Stability estimates for a class of neutral type systems with distributed time-varying delay components”, Adv Cont Discr Mod, 2025:1 (2025)  crossref
    2. G. V. Demidenko, I. I. Matveeva, Springer Proceedings in Mathematics & Statistics, 379, Functional Differential Equations and Applications, 2021, 145  crossref
    3. T. Yskak, “Stability of Solutions to One Class of Neutral Type Systems of Linear Autonomous Equations with Distributed Delay”, Lobachevskii J Math, 42:14 (2021), 3561  crossref
    4. T. Yskak, “On the stability of systems of linear differential equations of neutral type with distributed delay”, J. Appl. Industr. Math., 13:3 (2019), 575–583  mathnet  crossref  crossref  elib
    5. G. V. Demidenko, I. I. Matveeva, M. A. Skvortsova, “Estimates for solutions to neutral differential equations with periodic coefficients of linear terms”, Siberian Math. J., 60:5 (2019), 828–841  mathnet  crossref  crossref  isi  elib  elib
    6. G. V. Demidenko, I. I. Matveeva, “O robastnoi ustoichivosti reshenii lineinykh differentsialnykh uravnenii neitralnogo tipa s periodicheskimi koeffitsientami”, Sib. zhurn. industr. matem., 18:4 (2015), 18–29  mathnet  crossref  mathscinet  elib
    7. G. V. Demidenko, I. I. Matveeva, “On the exponential stability of solutions to one class of differential equations of neutral type”, J. Appl. Industr. Math., 8:4 (2014), 510–520  mathnet  crossref  mathscinet
    8. G. V. Demidenko, I. I. Matveeva, “Estimates for Solutions to One Class of Nonlinear Systems of Neutral Type with Several Delays”, J. Math. Sci., 213:6 (2016), 811–822  mathnet  crossref
    9. M. A. Skvortsova, “Asymptotic Properties of Solutions to Systems of Differential Equations of Neutral Type in Time-Varying Delay Case”, J. Math. Sci., 205:3 (2015), 455–463  mathnet  crossref
    10. M. A. Skvortsova, “Otsenki reshenii i oblasti prityazheniya nulevogo resheniya sistem kvazilineinykh uravnenii neitralnogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 10, 30–39  mathnet
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    Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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