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Rapidly varying solutions of a second-order differential equation with regularly and rapidly varying nonlinearities

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Abstract

For a second-order differential equation whose the right-hand side contains the sum of terms with regularly and rapidly varying nonlinearities, we establish the conditions of existence and asymptotic representations of rapidly varying solutions, as the argument tends to a singular point.

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Authors and Affiliations

  1. I. I. Mechnikov Odessa National University, Odessa, Ukraine

    Vyacheslav M. Evtukhov & Nataliya P. Kolun

Authors
  1. Vyacheslav M. Evtukhov
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  2. Nataliya P. Kolun
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Corresponding author

Correspondence to Vyacheslav M. Evtukhov.

Additional information

Translated from Russian by V. V. Kukhtin

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 15, No. 1, pp. 18–42 January–March, 2018.

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Evtukhov, V.M., Kolun, N.P. Rapidly varying solutions of a second-order differential equation with regularly and rapidly varying nonlinearities. J Math Sci 235, 15–34 (2018). https://doi.org/10.1007/s10958-018-4055-y

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  • DOI: https://doi.org/10.1007/s10958-018-4055-y

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