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On solutions of a second-order quasilinear differential system representable by Fourier series with slowly varying parameters

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Abstract

For a second-order quasilinear differential system whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove that, under certain conditions, there exists a particular solution with a similar structure in the case of purely imaginary roots of the characteristic equation for the matrix of coefficients of the linear part.

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Authors and Affiliations

  1. Odessa University, Odessa

    A. V. Kostin & S. A. Shchegolev

Authors
  1. A. V. Kostin
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  2. S. A. Shchegolev
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 654–664, May, 1998.

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Kostin, A.V., Shchegolev, S.A. On solutions of a second-order quasilinear differential system representable by Fourier series with slowly varying parameters. Ukr Math J 50, 741–753 (1998). https://doi.org/10.1007/BF02514327

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  • DOI: https://doi.org/10.1007/BF02514327

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