Skip to main content
SpringerLink
Log in

On Estimates of Solutions to One Class of Functional Difference Equations with Periodic Coefficients

  • Chapter
  • First Online:
Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy

Abstract

In the present paper, we consider a class of functional difference equations with periodic coefficients. We establish criteria for asymptotic stability of the zero solution to the equations and obtain estimates characterizing the decay rates of solutions to these equations at infinity.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Daleckii, Ju.L., Krein, M.G.: Stability of Solutions of Differential Equations in Banach Space. American Mathematical Society, Providence (1974)

    Google Scholar 

  2. Agarwal, R.P.: Difference Equations and Inequalities. Theory, Methods and Applications. Marcel Dekker, New York(1992)

    Google Scholar 

  3. Kocic, V.L., Ladas, G.: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. Kluwer Academic Publishers, Dordrecht (1993)

    Google Scholar 

  4. Elaydi, S.N.: An Introduction to Difference Equations. Springer, New York (1999)

    Google Scholar 

  5. Wilkinson, J.H.: The Algebraic Eigenvalue Problem. The Clarendon Press, Oxford University Press, New York (1988)

    Google Scholar 

  6. Akin, O., Bulgak, H.: Linear Difference Equations and Stability Theory. Selcuk University, Konya (1998)

    Google Scholar 

  7. Godunov, S.K.: Modern Aspects of Linear Algebra. American Mathematical Society, Providence (1998)

    Google Scholar 

  8. Aidyn, K., Bulgak, H., Demidenko, G.V.: Numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients. Sib. Math. J. 41(6), 1005–1014 (2000)

    Google Scholar 

  9. Aidyn, K., Bulgak, H., Demidenko, G.V.: Asymptotic stability of solutions to perturbed linear difference equations with periodic coefficients. Sib. Math. J. 43(3), 389–401 (2002)

    Google Scholar 

  10. Aidyn, K., Bulgak, H., Demidenko, G.V.: An estimate for the attraction domains of difference equations with periodic linear terms. Sib. Math. J. 45(6), 983–991 (2004)

    Google Scholar 

  11. Demidenko, G.V.: Matrix Equations. Novosibirsk State University, Novosibirsk (2009)

    Google Scholar 

  12. Demidenko, G.V.: Stability of solutions to difference equations with periodic coefficients in linear terms. J. Comput. Math. Optim. 6(1), 1–12 (2010)

    Google Scholar 

  13. Demidenko, G.V., Matveeva, I.I.: Stability of solutions to delay differential equations with periodic coefficients of linear terms. Sib. Math. J. 48(5), 824–836 (2007)

    Google Scholar 

  14. Demidenko, G.V., Matveeva, I.I.: On estimates of solutions to systems of differential equations of neutral type with periodic coefficients. Sib. Math. J. 55(5), 866–881 (2014)

    Google Scholar 

  15. Demidenko, G.V., Matveeva, I.I.: Estimates for solutions to a class of time-delay systems of neutral type with periodic coefficients and several delays. Electron. J. Qual. Theory Differ. Equ. 2015(83), 1–22 (2015)

    Google Scholar 

  16. Matveeva, I.I.: On exponential stability of solutions to periodic neutral-type systems. Sib. Math. J. 58(2), 264–270 (2017)

    Google Scholar 

  17. Matveeva, I.I.: On the exponential stability of solutions of periodic systems of the neutral type with several delays. Diff. Equ. 53(6), 725–735 (2017)

    Google Scholar 

  18. Demidenko, G.V., Matveeva, I.I., Skvortsova, M.A.: Estimates for solutions to neutral differential equations with periodic coefficients of linear terms. Sib. Math. J. 60(5), 828–841 (2019)

    Google Scholar 

  19. Matveeva, I.I.: Estimates of the exponential decay of solutions to linear systems of neutral type with periodic coefficients. J. Appl. Ind. Math. 13(3), 511–518 (2019)

    Google Scholar 

Download references

Acknowledgements

The authors are supported by the Russian Foundation for Basic Research (project no. 19-01-00754).

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Acad. Koptyug avenue 4, 630090, Novosibirsk, Russia

    G. V. Demidenko & I. I. Matveeva

  2. Novosibirsk State University, Pirogov street 1, 630090, Novosibirsk, 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 I. I. Matveeva .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Gennadii V. Demidenko

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Evgeniy Romenski

  3. Laboratory of Applied Mathematics, DICAM, University of Trento, Trento, Italy

    Eleuterio Toro

  4. Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy

    Michael Dumbser

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Demidenko, G.V., Matveeva, I.I. (2020). On Estimates of Solutions to One Class of Functional Difference Equations with Periodic Coefficients. In: Demidenko, G., Romenski, E., Toro, E., Dumbser, M. (eds) Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy. Springer, Cham. https://doi.org/10.1007/978-3-030-38870-6_14

Download citation

Publish with us

Policies and ethics

Search

Navigation