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 Computer Research and Modeling, 2015, Volume 7, Issue 4, Pages 821–833 (Mi crm262)

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Nonlinear boudary value problem in the case of parametric resonance

S. M. Chujko, O. V. Nesmelova, D. V. Sysoev

Donbass State Pedagogical University, 19 G. Batuka street, Donetsk region, Slavyansk, 84116, Ukraine

Abstract: We construct necessary and sufficient conditions for the existence of solution of seminonlinearmatrix boundary value problem for a parametric excitation system of ordinary differential equations. The convergent iteration algorithms for the construction of the solutions of the semi-nonlinear matrix boundary value problem for a parametric excitation system differential equations in the critical case have been found. Using the convergent iteration algorithms we expand solution of seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation in the neighborhood of the generating solution. Estimates for the value of residual of the solutions of the seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation are found.

Keywords: seminonlinear boundary value problem, matrix differential equations, generalized Green’s operator, parametric excitation.

 Funding Agency Grant Number State Fund for Fundamental Researches (Ukraine) 0112U0000372

DOI: https://doi.org/10.20537/2076-7633-2015-7-4-821-833

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Full text: http://crm.ics.org.ru/.../2342
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UDC: 517.9
Revised: 10.06.2015

Citation: S. M. Chujko, O. V. Nesmelova, D. V. Sysoev, “Nonlinear boudary value problem in the case of parametric resonance”, Computer Research and Modeling, 7:4 (2015), 821–833

Citation in format AMSBIB
\Bibitem{ChuNesSys15} \by S.~M.~Chujko, O.~V.~Nesmelova, D.~V.~Sysoev \paper Nonlinear boudary value problem in the case of parametric resonance \jour Computer Research and Modeling \yr 2015 \vol 7 \issue 4 \pages 821--833 \mathnet{http://mi.mathnet.ru/crm262} \crossref{https://doi.org/10.20537/2076-7633-2015-7-4-821-833}