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Averaging in Boundary-Value Problems for Systems of Differential and Integrodifferential Equations

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Ukrainian Mathematical Journal Aims and scope

The averaging method is applied to the investigation of the problem of existence of solutions of boundary-value problems for systems of differential and integrodifferential equations. It is shown that if the averaged boundary-value problem has a solution, then the original problem also has a solution. Note that, in this case, the system obtained as a result of averaging of a system of integrodifferential equations has the form of a simpler system of ordinary differential equations.

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Authors and Affiliations

  1. T. Shevchenko Kiev National University, Kiev, Ukraine

    A. N. Stanzhitskii

  2. Zhubanov Aktyubinsk Regional State University, Aktobe, Kazakhstan

    S. T. Mynbayeva

  3. Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan

    S. T. Mynbayeva

  4. Podol’skii Agrarian-Technical University, Kamenets-Podol’skii, Ukraine

    N. A. Marchuk

Authors
  1. A. N. Stanzhitskii
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  2. S. T. Mynbayeva
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  3. N. A. Marchuk
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Corresponding author

Correspondence to A. N. Stanzhitskii.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 2, pp. 245–266, February, 2020.

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Stanzhitskii, A.N., Mynbayeva, S.T. & Marchuk, N.A. Averaging in Boundary-Value Problems for Systems of Differential and Integrodifferential Equations. Ukr Math J 72, 277–301 (2020). https://doi.org/10.1007/s11253-020-01781-2

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  • DOI: https://doi.org/10.1007/s11253-020-01781-2

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