Ukrainian Mathematical Journal

, Volume 29, Issue 6, pp 554–563 | Cite as

The problem of justifying the averaging method for second-order equations with impulsive action

  • Yu. A. Mitropol'skii
  • A. M. Samoilenko
  • N. A. Perestyuk


Average Method Impulsive Action 
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Literature cited

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    N. M. Krylov and N. N. Bogolyubov, Application of Methods of Nonlinear Mechanics and the Theory of Stationary Oscillations [in Russian], Izd. Vceukrainskoi Akad. Nauk, Kiev (1934).Google Scholar
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    N. M. Krylov and N. N. Bologyubov, Introduction to Nonlinear Mechanics [in Russian], Izd. Akad. Nauk UkrSSR, Kiev (1937).Google Scholar
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    N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Third Edition, Fizmatgiz, Moscow (1963).Google Scholar
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    Yu. A, Mitropol'skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).Google Scholar
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    A. M. Samoilenko, “The averaging method in systems with impulsive action,” in: Mathematical Physics [in Russian], No. 9, Naukova Dumka, Kiev (1971), pp. 101–117.Google Scholar
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    A. M. Samoilenko and N. A. Perestyuk, “On the question of justification of the averaging method for second-order differential equations with impulsive action,” in: Nonlinear Oscillations aad Stability of Motion [in Russian], Inst. Mat. Akad. Nauk UkrSSR, Kiev (1973), pp. 273–282.Google Scholar
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    A. N. Filatov and L. V. Sharova, Integral Inequalities and Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1976).Google Scholar
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    A. M. Samoilenko, “On the preservation of the invariant torus under perturbation,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 6, 1219–1240 (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Yu. A. Mitropol'skii
    • 1
    • 2
  • A. M. Samoilenko
    • 1
    • 2
  • N. A. Perestyuk
    • 1
    • 2
  1. 1.Mathematics InstituteAcademy of Sciences of the Ukrainian SSRUkraine
  2. 2.Kiev State UniversityUSSR

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