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Weakly Nonlinear Matrix Boundary-Value Problem in the Case of Parametric Resonance

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We establish necessary and sufficient conditions for the existence of solutions of a nonlinear matrix boundary-value problem for a system of ordinary differential equations in the case of parametric resonance. We construct a convergent iterative scheme for finding approximate solutions of the problem. As an example of application of the proposed iterative scheme, we obtain approximations to the solutions of a periodic boundary-value problem for the Riccati-type equation with parametric perturbation. To check the accuracy of the obtained approximations, we introduce residuals in the original equation.

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Authors and Affiliations

  1. Donbass State Pedagogic University, General Batyuk Str., 19, Slavyansk, Donetsk Region, 84116, Ukraine

    S. M. Chuiko, A. S. Chuiko & D. V. Sysoev

Authors
  1. S. M. Chuiko
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  2. A. S. Chuiko
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  3. D. V. Sysoev
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Translated from Neliniini Kolyvannya, Vol. 19, No. 2, pp. 276–288, April–June, 2016.

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Chuiko, S.M., Chuiko, A.S. & Sysoev, D.V. Weakly Nonlinear Matrix Boundary-Value Problem in the Case of Parametric Resonance. J Math Sci 223, 337–350 (2017). https://doi.org/10.1007/s10958-017-3359-7

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  • DOI: https://doi.org/10.1007/s10958-017-3359-7

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