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Ukrainian Mathematical Journal

, Volume 23, Issue 2, pp 125–132 | Cite as

On the principle of averaging for second-order hyperbolic equations with functionally perturbed argument

  • D. G. Korenevskii
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  • 22 Downloads

Keywords

Hyperbolic Equation 
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Literature cited

  1. 1.
    N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).Google Scholar
  2. 2.
    Yu. A. Mitropol'skii, Lectures on the Method of Averaging in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1966).Google Scholar
  3. 3.
    Yu. A. Mitropol'skii, Problems of an Asymptotic Theory of Nonstationary Vibrations [in Russian], Nauka, Moscow (1964).Google Scholar
  4. 4.
    V. M. Volosov, “Averaging in systems of ordinary differential equations,” Usp. Mat. Nauk.,17, No. 6 (1962).Google Scholar
  5. 5.
    M. M. Khapaev, “On the method of averaging in problems related to averaging,” Differentsial'nye Uravneniya,2, No. 5 (1966).Google Scholar
  6. 6.
    V. P. Rubanik, Vibrations in Quasilinear Systems with Retardation [in Russian], Nauka, Moscow (1969).Google Scholar
  7. 7.
    V. I. Fodchuk, “The method of averaging for differential-difference equations of neutral type,” Ukr. Matem. Zh.,20, No. 2 (1968).Google Scholar
  8. 8.
    V. I. Fodchuk, “On the continuous dependence of the solutions of differential equations with retarded argument on a parameter,” Ukr. Matem. Zh.,16, No. 2 (1964).Google Scholar
  9. 9.
    V. M. Volosov, G. N. Medvedev, and B. I. Morgunov, “On the application of the method of averaging to various systems with perturbed argument,” Vestnik MGU (1969).Google Scholar
  10. 10.
    R. Z. Khas'minskii, “On the principle of averaging for parabolic and elliptic differential equations and Markov processes with small diffusion,” Teoriya Veroyatnostei i ee Primeneniya, No. 1 (1963).Google Scholar
  11. 11.
    Yu. A. Mitropol'skii and V. I. Fodchuk, “Asymptotic methods of nonlinear mechanics with reference to nonlinear differential equations with a retarded argument,” Ukr. Matem. Zh.,18, No. 3 (1966).Google Scholar
  12. 12.
    Yu. I. Neimark and L. Z. Fishman, “On the behavior in the large of the phase trajectories of quasilinear differential equations with retarded argument,” Izv. Vuzov, Radiofizika, No. 6 (1966).Google Scholar
  13. 13.
    D. G. Korenevskii and S. F. Feshchenko, “Existence and uniqueness theorem for the Cauchy problem for a hyperbolic equation with selfregulated retardation,” Differentsial'nye Uravneniya,3, No. 8 (1967).Google Scholar
  14. 14.
    E. F. Beckenbach and R. Bellmann, Inequalities, Springer, Berlin (1965).Google Scholar
  15. 15.
    M. Kiselevich, “Bogolyubov-type theorem for hyperbolic equations,” Ukr. Matem. Zh.,22, No. 3 (1970).Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • D. G. Korenevskii
    • 1
  1. 1.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRUSSR

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