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Computer Research and Modeling, 2014, Volume 6, Issue 1, Pages 27–43
DOI: https://doi.org/10.20537/2076-7633-2014-6-1-27-43 (Mi crm302) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Periodic boudary-value problem for Hill's equation in the case of parametric resonance

S. M. Chujko, O. V. Starkova, P. V. Kulish

Donbass State Pedagogical University, 19 G. Batuka street, Donetsk region, Slavyansk, 84116, Ukraine
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DOI: https://doi.org/10.20537/2076-7633-2014-6-1-27-43
Abstract: Necessary and sufficient conditions for the existence of solutions of nonlinear nonautonomous periodic problem for Hill's equation in the case of parametric resonance. A characteristic feature of the task is the need of finding, as desired solution, and the corresponding eigenfunction, which ensures solvability of the periodic problem for Hill's equation in the case of parametric resonance. To construct solutions of the periodic problem for Hill's equation and the corresponding eigenfunction in the case of parametric resonance propose diterative scheme, based on the method of simple iterations with used list-square technics.
Keywords: nonlinear nonautonomous periodic boudary-value problem, Hill’s equation, the case of parametricresonance, he method of simple iterations.
Funding agency Grant number
State Fund for Fundamental Researches (Ukraine) 0112U0000372
Received: 27.10.2013
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. M. Chujko, O. V. Starkova, P. V. Kulish, “Periodic boudary-value problem for Hill's equation in the case of parametric resonance”, Computer Research and Modeling, 6:1 (2014), 27–43
Citation in format AMSBIB
\Bibitem{ChuStaKul14}
\by S.~M.~Chujko, O.~V.~Starkova, P.~V.~Kulish
\paper Periodic boudary-value problem for Hill's equation in the case of parametric resonance
\jour Computer Research and Modeling
\yr 2014
\vol 6
\issue 1
\pages 27--43
\mathnet{http://mi.mathnet.ru/crm302}
\crossref{https://doi.org/10.20537/2076-7633-2014-6-1-27-43}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Computer Research and Modeling
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