Ukrainian Mathematical Journal

, Volume 60, Issue 9, pp 1498–1508 | Cite as

Periodic solutions of linear impulsive differential inclusions

  • N. V. Skripnik

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


Periodic Solution Differential Inclusion Contraction Operator Impulsive Differential Equation Quasivariational Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. I. Panasyuk and V. V. Panasyuk, Asymptotic Optimization of Nonlinear Control Systems [in Russian], Belorussian University, Minsk (1977).Google Scholar
  2. 2.
    A. A. Tolstonogov, Differential Inclusions in a Banach Space [in Russian], Nauka, Novosibirsk (1986).zbMATHGoogle Scholar
  3. 3.
    R. J. Aumann, “Integrals of set-valued functions,” J. Math. Anal. Appl., 12, No. 1, 1–12 (1965).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).Google Scholar
  5. 5.
    V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989).zbMATHGoogle Scholar
  6. 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).zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    P. J. Watson, “Impulsive differential inclusions,” Nonlin. World, 4, No. 4, 395–402 (1997).zbMATHGoogle Scholar
  8. 8.
    N. V. Plotnikova, “Periodic solutions of linear impulsive differential inclusions,” Nelin. Kolyvannya, 7, No. 4, 495–515 (2004).zbMATHMathSciNetGoogle Scholar
  9. 9.
    V. I. Blagodatskikh and A. F. Filippov, “Differential inclusions and optimal control,” Tr. Mat. Inst. Akad. Nauk SSSR, 169, 194–252 (1985).zbMATHMathSciNetGoogle Scholar
  10. 10.
    V. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).Google Scholar
  11. 11.
    A. A. Lyapunov, “On completely additive vector functions,” Izv. Akad. Nauk SSSR, Ser. Mat., No. 6, 465–478 (1940).Google Scholar
  12. 12.
    C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities. Applications to Free Boundary Problems, Wiley, New York (1984).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • N. V. Skripnik
    • 1
  1. 1.Odessa National UniversityOdessaUkraine

Personalised recommendations