Differential Equations

, Volume 48, Issue 8, pp 1177–1179 | Cite as

Asymptotic integration of a system of differential equations with high-frequency terms in the critical case

  • N. T. Do
  • V. B. Levenshtam
Short Communications

Abstract

We construct the complete asymptotics of a periodic solution of a linear normal system of differential equations with high-frequency coefficients. We study the Lyapunov stability and instability of that solution. More specifically, we consider the critical case in which the matrix coefficient of the formally averaged stationary system has one eigenvector and one generalized (in the Vishik-Lyusternik sense) associated vector.

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References

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    Bogolyubov, N.N. and Mitropol’skii, Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii (Asymptotic Methods in the Theory of Nonlinear Oscillations), Moscow: Nauka, 1974.MATHGoogle Scholar
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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • N. T. Do
    • 1
    • 2
  • V. B. Levenshtam
    • 1
    • 2
  1. 1.South Federal UniversityRostov-on-DonRussia
  2. 2.South Mathematical InstituteVladikavkazRussia

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