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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/crm302
https://www.mathnet.ru/eng/crm/v6/i1/p27
This publication is cited in the following 1 articles:
S. M. Chuiko, O. V. Nesmelova (Starkova), D. V. Sysoev, “Nelineinaya matrichnaya kraevaya zadacha v sluchae parametricheskogo rezonansa”, Kompyuternye issledovaniya i modelirovanie, 7:4 (2015), 821–833
Citation in format AMSBIB
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