Nonlinear Oscillations

, Volume 7, Issue 4, pp 454–460 | Cite as

Existence of Green-Samoilenko Functions of Some Linear Extensions of Dynamical Systems

  • H. M. Kulyk
  • V. L. Kulyk


We study the problem of the existence of a Green-Samoilenko function for some linear extensions of dynamical systems.


Differential Equation Dynamical System Partial Differential Equation Ordinary Differential Equation Functional Equation 
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    Yu. A. Mitropol’skii, A. M. Samoilenko, and V. L. Kulik, Investigation of Dichotomy of Linear Systems of Differential Equations Using Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
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    A. M. Samoilenko, “On the existence of a unique Green function for the linear extension of a dynamical system on a torus,” Ukr. Mat. Zh., 53, No.4, 513–521 (2001).Google Scholar
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    A. A. Boichuk, “A condition for the existence of a unique Green-Samoilenko function for the problem of invariant torus,” Ukr. Mat. Zh., 53, No.4, 556–559 (2001).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • H. M. Kulyk
    • 1
  • V. L. Kulyk
    • 2
    • 3
  1. 1.Kyiv Polytechnic InstituteKyivUkraine
  2. 2.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  3. 3.Silesian University of TechnologyPoland

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