Ukrainian Mathematical Journal

, Volume 50, Issue 1, pp 100–107 | Cite as

On integral manifolds of oscillating systems with slowly varying frequencies

  • R. I. Petryshyn
  • L. M. Lakusta
Article
  • 13 Downloads

Abstract

By using averages of functions, we construct the integral manifold of an oscillating system that passes through resonances in the course of its evolution. We investigate the smoothness of the integral manifold and obtain estimates for its partial derivatives.

Keywords

Partial Derivative Cauchy Problem Bounded Domain Vary Frequency Fourier Coefficient 

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References

  1. 1.
    A. M. Samoilenko and R. I. Petryshyn, “On the integral manifolds of multifrequency oscillating systems,” Izv. Akad. Nauk SSSR, Ser. Mat., 54, No. 2, 378–395 (1990).Google Scholar
  2. 2.
    R. I. Petryshyn, Investigation of Oscillating Systems with Slowly Varying Frequencies bx the Averaging Method [in Ukrainian], Doctoral-Degree Thesis (Physics and Mathematics), Kiev (1995).Google Scholar
  3. 3.
    V. A. Pliss, Integral Sets for Periodic Systems of Differential Equations [in Russian], Nauka, Moscow (1977).Google Scholar
  4. 4.
    S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • R. I. Petryshyn
    • 1
  • L. M. Lakusta
    • 1
  1. 1.Chernovtsy UniversityChernovtsy

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