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Ufimsk. Mat. Zh., 2009, Volume 1, Issue 2, Pages 29–52 (Mi ufa10)  

This article is cited in 4 scientific papers (total in 4 papers)

Averaging method for the problems on asymptotics at infinity

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: A nonlinear non-autonomous system of two ordinary differential equations is considered. It is assumed that the equations corresponding to the principal part in the asymptotics at infinity are written in the action–angle variable. In the case where the lower terms in the equation periodically depend on the angle the asymptotic expansion at infinity of two parametric family of solutions is constructed.

Keywords: nonlinear differential equations, asymptotics, averaging.

Full text: PDF file (514 kB)
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Bibliographic databases:

UDC: 517.956.226
Received: 08.05.2009

Citation: L. A. Kalyakin, “Averaging method for the problems on asymptotics at infinity”, Ufimsk. Mat. Zh., 1:2 (2009), 29–52

Citation in format AMSBIB
\Bibitem{Kal09}
\by L.~A.~Kalyakin
\paper Averaging method for the problems on asymptotics at infinity
\jour Ufimsk. Mat. Zh.
\yr 2009
\vol 1
\issue 2
\pages 29--52
\mathnet{http://mi.mathnet.ru/ufa10}
\zmath{https://zbmath.org/?q=an:1240.34226}
\elib{http://elibrary.ru/item.asp?id=12501230}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. A. Sultanov, “Funktsii Lyapunova dlya neavtonomnykh sistem blizkikh k gamiltonovym”, Ufimsk. matem. zhurn., 2:4 (2010), 88–98  mathnet  zmath
    2. L. A. Kalyakin, “Lyapunov Functions in Justification Theorems for Asymptotics”, Math. Notes, 98:5 (2015), 752–764  mathnet  crossref  crossref  mathscinet  isi  elib
    3. L. A. Kalyakin, “Uravnenie Penleve-II kak model rezonansnogo vzaimodeistviya ostsillyatorov”, Tr. IMM UrO RAN, 23, no. 2, 2017, 104–116  mathnet  crossref  elib
    4. L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, Theoret. and Math. Phys., 194:3 (2018), 331–346  mathnet  crossref  crossref  isi  elib
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