Ukrainian Mathematical Journal

, Volume 53, Issue 8, pp 1266–1289 | Cite as

On the Existence of Periodic Solutions for Certain Classes of Systems of Differential Equations with Random Pulse Influence

  • N. A. Perestyuk
  • A. M. Samoilenko
  • A. N. Stanzhitskii

Abstract

We establish conditions for the existence of periodic solutions for systems of differential equations with random right-hand side and random pulse influence at fixed times. We consider the case of small pulse perturbation and weakly nonlinear systems.

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REFERENCES

  1. 1.
    R. Z. Khas'minskii, Stability of Systems of Differential Equations under Random Perturbation of Their Parameters [in Russian], Nauka, Moscow (1969).Google Scholar
  2. 2.
    A. M. Samoilenko and M. O. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).Google Scholar
  3. 3.
    V. B. Kolmanovskii, “Stationary solutions of delay equations,” Probl. Per. Inform., 3, No. 1, 64-72 (1967).Google Scholar
  4. 4.
    V. I. Zubov, Stability of Motion [in Russian], Vysshaya Shkola, Moscow (1973).Google Scholar
  5. 5.
    A. Ya. Dorogovtsev, Periodic and Stationary Modes of Finite-Dimensional Deterministic and Stochastic Dynamical Systems [in Russian], Vyshcha Shkola, Kiev (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • N. A. Perestyuk
    • 1
  • A. M. Samoilenko
    • 2
  • A. N. Stanzhitskii
    • 1
  1. 1.Kiev UniversityKiev
  2. 2.Institute of MathematicsUkrainian Academy of SciencesKiev

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