Skip to main content
SpringerLink
Log in

On invariance of some properties of solutions under perturbation of a pulse system of differential equations

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Sufficient conditions for the invariance of boundedness and stability properties of solutions under perturbation of a pulse system of differential equations are established.

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

References

  1. A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  2. A. Strauss and G. A. Yorke, “Perturbing uniform asymptotically stable nonlinear systems,”J. Different. Equat.,6, No. 3, 452–483 (1969).

    Google Scholar 

  3. R. Bernfeld, “Perturbing uniform ultimate bounded differential systems,”SIAM J. Math. Anal.,3, No. 2, 358–370 (1972).

    Google Scholar 

  4. Yu. A. Mitropol'skii, A. M. Samoilenko, and N. A. Perestyuk, “On justification of the averaging method for equations of the second order with pulse influence,”Ukr. Mat. Zh.,29, No. 6, 750–762 (1977).

    Google Scholar 

  5. A. M. Samoilenko and N. A. Perestyuk, “On stability of solutions of systems with pulse influence,”Differents. Uravn.,17, No. 11, 1995–2002 (1981).

    Google Scholar 

  6. S. I. Gurgula and N. A. Perestyuk, “The Lyapunov's second method in systems with pulse influence,”Dokl. Akad. Nauk Ukr. SSR, No. 10, 11–14 (1982).

    Google Scholar 

  7. O. S. Chernikova, “On boundedness of solutions of systems of differential equations with pulse influence,”Ukr. Mat. Zh.,38, No. 1, 124–128 (1986).

    Google Scholar 

  8. Yu. A. Mitropol'skii, N. A. Perestyuk, and O. S. Chernikova, “Convergence of systems of differential equations with pulse influence,”Dokl. Akad. Nauk Ukr. SSR, No. 11, 11–15 (1983).

    Google Scholar 

  9. A. Strauss and G. A. Yorke, “Perturbations theorems for ordinary differential equations,”J. Different. Equat.,3, No. 1, 15–30 (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev University, Kiev

    N. A. Perestyuk

  2. Kiev Army Institute, Kiev

    O. S. Chernikova

Authors
  1. N. A. Perestyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. S. Chernikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1707–1713, December, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perestyuk, N.A., Chernikova, O.S. On invariance of some properties of solutions under perturbation of a pulse system of differential equations. Ukr Math J 46, 1899–1906 (1994). https://doi.org/10.1007/BF01063174

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01063174

Keywords

Search

Navigation