Усреднение в краевых задачах для систем дифференциальных и интегро-дифференциальных уравнений

S. T. Mynbayeva; A. N. Stanzhitskii; N. A. Marchuk

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

Abstract

References