Nonlinear Oscillations

, 13:429 | Cite as

Construction of particular asymptotic solutions of linear degenerate systems of delay differential equations


We construct particular asymptotic solutions of a linear system of delay differential equations with slowly varying coefficients in the case where the characteristic equation has a multiple root.


Asymptotic Solution Delay Differential Equation Mathematical Induction Multiple Root Taylor Formula 
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  1. 1.
    S. F. Feshchenko, N. I. Shkil’, Yu. P. Pidchenko, and N. A. Sotnichenko, Asymptotic Methods in the Theory of Linear Differential Equations with Deviating Argument [in Russian], Naukova Dumka, Kiev (1981).Google Scholar
  2. 2.
    A. M. Samoilenko, M. I. Shkil’, and V. P. Yakovets’, Linear Systems of Degenerate Differential Equations [in Ukrainian], Vyshcha Shkola, Kyiv (2000).Google Scholar
  3. 3.
    P. F. Samusenko, “Construction of asymptotic solutions of systems of differential equations with deviating argument and degenerate matrix of coefficients of derivatives,” Nelin. Kolyvannya, 5, No. 4, 527–539 (2002).MATHMathSciNetGoogle Scholar
  4. 4.
    V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 3, Part 1, Nauka, Moscow (1974).Google Scholar
  5. 5.
    Y. Sibuya, “Some global properties of functions of one variable,” Math. Anal., 161, No. 1, 67–77 (1965).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Drahomanov National Pedagogic UniversityKyivUkraine

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