Skip to main content
SpringerLink
Log in

Estimates for Solutions of One Class of Nonlinear Neutral Type Systems with Several Delays

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity. Bibliography: 14 titles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. E. El’sgol’ts and S. B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments [in Russian], Nauka, Moscow (1971); English transl.: Academic Press, New York etc. (1973).

  2. G. V. Demidenko and I. I. Matveeva, “Asymptotic properties of solutions to delay differential equations” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 5, No. 3, 20–28 (2005).

  3. G. V. Demidenko and I. I. Matveeva, “Stability of solutions to delay differential equations with periodic coefficients of linear terms” [in Russian], Sib. Mat. Zh. 48, No. 5, 1025–1040 (2007); English transl.: Sib. Mat. J. 48, No. 5, 824–836 (2007).

  4. G. V. Demidenko, “Stability of solutions to linear differential equations of neutral type” J. Anal. Appl. 7, No. 3, 119–130 (2009).

    MathSciNet  MATH  Google Scholar 

  5. G. V. Demidenko, T. V. Kotova, and M. A. Skvortsova, “Stability of solutions to differential equations of neutral type” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 10, No. 3, 17–29 (2010); English transl.: J. Math. Sci. 186, No. 3, 394–406 (2012).

  6. I. I. Matveeva and A. A. Shcheglova, “Some estimates of the solutions to time-delay differential equations with parameters” [in Russian], Sib. Zh. Ind. Mat. 14, No. 1, 83–92 (2011); English transl.: J. Appl. Ind. Math. 5, No. 3, 391–399 (2011).

  7. G. V. Demidenko, E. S. Vodopyanov, and M. A. Skvortsova, “Estimates of solutions to the linear differential equations of neutral type with several delays of the argument” [in Russian], Sib. Zh. Ind. Mat. 16, No. 3, 53–60 (2013); English transl.: J. Appl. Ind. Math. 7, No. 4, 472–479 (2013).

  8. I. I. Matveeva, “Estimates of solutions to a class of systems of nonlinear delay differential equations” [in Russian], Sib. Zh. Ind. Mat. 16, No. 3, 122–132 (2013); English transl.: J. Appl. Ind. Math. 7, No. 4, 557–566 (2013).

  9. G. V. Demidenko and I. I. Matveeva, “On exponential stability of solutions to one class of systems of differential equations of neutral type” [in Russian], Sib. Zh. Ind. Mat. 17, No. 3, 59–70 (2014); English transl.: J. Appl. Ind. Math. 8, No. 4, 510–520 (2014).

  10. G. V. Demidenko and I. I. Matveeva, “Estimates for solutions to linear systems of neutral type with several delays” J. Anal. Appl. 12, No. 1–2, 37–52 (2014).

    MathSciNet  Google Scholar 

  11. J. Hale, Theory of Functional Differential Equations, Springer, New York etc. (1977).

    Book  MATH  Google Scholar 

  12. D. G. Korenevskij, Stability of Dynamical Systems under Random Perturbations of Parameters. Algebraic Criteria [in Russian], Naukova Dumka, Kiev (1989).

  13. V. B. Kolmanovskii and A. D. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Acad., Dordrecht (1999).

    Book  MATH  Google Scholar 

  14. V. L. Kharitonov, Time-Delay Systems. Lyapunov Functionals and Matrices, Birkh¨auser, New York (2013).

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4, pr. Akad. Koptyuga, Novosibirsk, 630090, Russia

    G. V. Demidenko & I. I. Matveeva

  2. Novosibirsk State University, 2, ul. Pirogova, Novosibirsk, 630090, Russia

    G. V. Demidenko & I. I. Matveeva

Authors
  1. G. V. Demidenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. I. Matveeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. V. Demidenko.

Additional information

Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 14, No. 4, 2014, pp. 32–43.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Demidenko, G.V., Matveeva, I.I. Estimates for Solutions of One Class of Nonlinear Neutral Type Systems with Several Delays. J Math Sci 213, 811–822 (2016). https://doi.org/10.1007/s10958-016-2742-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-016-2742-0

Keywords

Search

Navigation