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A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters

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Abstract

For a quasilinear second-order differential system, whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove, under certain conditions, the existence of a particular solution having a similar structure. This result is obtained in the case where the characteristic equation possesses purely imaginary roots, which satisfy a certain resonance relation.

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References

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Authors and Affiliations

  1. Odessa University, Odessa

    S. A. Shchegolev

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  1. S. A. Shchegolev
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 285–288, February, 1999.

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Shchegolev, S.A. A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters. Ukr Math J 51, 324–327 (1999). https://doi.org/10.1007/BF02513488

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  • DOI: https://doi.org/10.1007/BF02513488

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