Skip to main content
SpringerLink
Log in

Periodic solutions of linear impulsive differential inclusions

  • Published:
Ukrainian Mathematical Journal Aims and scope

We establish sufficient conditions for the existence of periodic R-solutions of linear differential inclusions with impulses at fixed times.

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. A. I. Panasyuk and V. V. Panasyuk, Asymptotic Optimization of Nonlinear Control Systems [in Russian], Belorussian University, Minsk (1977).

    Google Scholar 

  2. A. A. Tolstonogov, Differential Inclusions in a Banach Space [in Russian], Nauka, Novosibirsk (1986).

    MATH  Google Scholar 

  3. R. J. Aumann, “Integrals of set-valued functions,” J. Math. Anal. Appl., 12, No. 1, 1–12 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  5. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989).

    MATH  Google Scholar 

  6. L. Erbe and W. Krawcewicz, “Existence of solutions to boundary value problems for impulsive second order differential inclusions,” Rocky Mt. J. Math., 22, No. 2, 519–539 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  7. P. J. Watson, “Impulsive differential inclusions,” Nonlin. World, 4, No. 4, 395–402 (1997).

    MATH  Google Scholar 

  8. N. V. Plotnikova, “Periodic solutions of linear impulsive differential inclusions,” Nelin. Kolyvannya, 7, No. 4, 495–515 (2004).

    MATH  MathSciNet  Google Scholar 

  9. V. I. Blagodatskikh and A. F. Filippov, “Differential inclusions and optimal control,” Tr. Mat. Inst. Akad. Nauk SSSR, 169, 194–252 (1985).

    MATH  MathSciNet  Google Scholar 

  10. V. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  11. A. A. Lyapunov, “On completely additive vector functions,” Izv. Akad. Nauk SSSR, Ser. Mat., No. 6, 465–478 (1940).

  12. C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities. Applications to Free Boundary Problems, Wiley, New York (1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Odessa National University, Odessa, Ukraine

    N. V. Skripnik

Authors
  1. N. V. Skripnik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1287–1296, September, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skripnik, N.V. Periodic solutions of linear impulsive differential inclusions. Ukr Math J 60, 1498–1508 (2008). https://doi.org/10.1007/s11253-009-0136-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-009-0136-x

Keywords

Search

Navigation