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Autonomous Noetherian Boundary-Value Problem in the Case of Parametric Resonance

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We establish constructive conditions for the solvability of a nonlinear autonomous boundary-value problem in the presence of parametric resonance and develop a scheme for the construction of solutions of this problem. We propose a convergent iterative algorithm for finding approximate solutions of the nonlinear autonomous Noetherian boundary-value problem for a system of ordinary differential equations in the case of parametric resonance. As an example of application of the constructed iterative algorithm, we determine approximate solutions of the periodic boundary-value problem for the autonomous Duffing-type equation with parametric perturbation.

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Authors and Affiliations

  1. Donbas State Pedagogic University, General Batyuk Str., 19, Slov’yans’k, 84116, Ukraine

    S. M. Chuiko & O. S. Chuiko

  2. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Dobrovol’s’kyi Str., 1, Slov’yans’k, 84109, Ukraine

    O. V. Nesmelova

Authors
  1. S. M. Chuiko
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  2. O. V. Nesmelova
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  3. O. S. Chuiko
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Correspondence to S. M. Chuiko.

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Translated from Neliniini Kolyvannya, Vol. 23, No. 1, pp. 134–144, January–March, 2020.

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Chuiko, S.M., Nesmelova, O.V. & Chuiko, O.S. Autonomous Noetherian Boundary-Value Problem in the Case of Parametric Resonance. J Math Sci 256, 713–725 (2021). https://doi.org/10.1007/s10958-021-05455-7

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  • DOI: https://doi.org/10.1007/s10958-021-05455-7

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