Skip to main content
SpringerLink
Log in

On the Existence of Periodic Solutions to One Class of Systems of Nonlinear Differential Equations

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

A class of systems of nonlinear differential equations is considered. It is assumed that the linear part of the system has constant coefficients and is exponentially dichotomous. Conditions for the existence of periodic solutions are established and their stability is proved for small perturbations of the coefficients of the linear part and nonlinear terms.

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. Ju. L. Daleckii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space (Am. Math. Soc., Providence, RI, 1974).

  2. A. Ya. Bulgakov, ‘‘Substantiation of guaranteed accuracy for the selection of invariant subspaces of nonselfadjoint matrices,’’ Tr. Inst. Mat. 15, 12–93 (1989).

    MATH  Google Scholar 

  3. S. K. Godunov, Modern Aspects of Linear Algebra (Nauch. Kniga, Novosibirsk, 1997) [in Russian].

    MATH  Google Scholar 

  4. G. V. Demidenko, Matrix Equations (Novosib. Gos. Univ., Novosibirsk, 2009) [in Russian].

    Google Scholar 

  5. G. V. Demidenko, ‘‘On a functional approach to constructing projections onto invariant subspaces of matrices,’’ Sib. Math. J. 39, 683–699 (1998).

    Article  Google Scholar 

  6. G. V. Demidenko, ‘‘Systems of differential equations with periodic coefficients,’’ J. Appl. Ind. Math. 8, 20–27 (2014).

    Article  MathSciNet  Google Scholar 

Download references

Funding

The work was supported by the Russian Foundation for Basic Research (project no. 18-29-10086).

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    G. V. Demidenko

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    G. V. Demidenko

Authors
  1. G. V. Demidenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. V. Demidenko.

Additional information

(Submitted by A. B. Muravnik)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Demidenko, G.V. On the Existence of Periodic Solutions to One Class of Systems of Nonlinear Differential Equations. Lobachevskii J Math 42, 3336–3343 (2021). https://doi.org/10.1134/S1995080222020044

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080222020044

Keywords:

Search

Navigation