Averaging in boundary-value problems for systems of differential and integrodifferential equations

  • S. T. Mynbayeva K.Zhubanov Aktobe Regional State University; Institute of Mathematics and Mathematical Modeling
  • A. N. Stanzhitskii Kiyev. nats. un-t im. T. Shevchenko
  • N. A. Marchuk Podil. agrarian-technical University of Kamyanets-Podilsky
Keywords: Averaging, boundary value problem, Volterra type, convergence, variation

Abstract

UDC 517.9

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.  It is worth noting 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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Published
15.02.2020
How to Cite
MynbayevaS. T., StanzhitskiiA. N., and MarchukN. A. “Averaging in Boundary-Value Problems for Systems of Differential and Integrodifferential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 2, Feb. 2020, pp. 245-66, http://umj.imath.kiev.ua/index.php/umj/article/view/1071.
Section
Research articles