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Matematicheskie Zametki, 2005, Volume 78, Issue 1, Pages 85–97
DOI: https://doi.org/10.4213/mzm2564 (Mi mzm2564) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Asymptotics of Bounded-at-Infinity Solutions of the Principal Resonance Equation

L. A. Kalyakin, Yu. Yu. Bagderina

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Full-text PDF (260 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm2564
Abstract: We consider a system of six nonlinear differential equations obtained by averaging fast forced oscillations. The main result consist in the construction of the asymptotics at infinity for the general solution with bounded amplitudes. We show that the structure of asymptotic series depends on the parameters so that the coefficients of the series vary in jumps on the resonance set.
Received: 20.05.2004
Revised: 17.12.2004
English version:
Mathematical Notes, 2005, Volume 78, Issue 1, Pages 76–87
DOI: https://doi.org/10.1007/s11006-005-0101-4
Bibliographic databases:
UDC: 517.928
Language: Russian
Citation: L. A. Kalyakin, Yu. Yu. Bagderina, “Asymptotics of Bounded-at-Infinity Solutions of the Principal Resonance Equation”, Mat. Zametki, 78:1 (2005), 85–97; Math. Notes, 78:1 (2005), 76–87
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm2564
  • https://www.mathnet.ru/eng/mzm/v78/i1/p85
    • This publication is cited in the following 3 articles:
    1. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. S. G. Glebov, O. M. Kiselev, V. A. Lazarev, “The autoresonance threshold in a system of weakly coupled oscillators”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S111–S123  mathnet  crossref  elib
    3. L. A. Kalyakin, “Resonance Capture in a Nonlinear System”, Theoret. and Math. Phys., 144:1 (2005), 944–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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