Nonlinear boudary value problem in the case of parametric resonance

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We construct necessary and sufficient conditions for the existence of solution of seminonlinear matrix 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
Citation in English: Chujko S.M., Nesmelova (Starkova) O.V., Sysoev D.V. Nonlinear boudary value problem in the case of parametric resonance // Computer Research and Modeling, 2015, vol. 7, no. 4, pp. 821-833
Citation in English: Chujko S.M., Nesmelova (Starkova) O.V., Sysoev D.V. Nonlinear boudary value problem in the case of parametric resonance // Computer Research and Modeling, 2015, vol. 7, no. 4, pp. 821-833
DOI: 10.20537/2076-7633-2015-7-4-821-833
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