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The method of averaging byBihun, Y.Petryshyn, R.Skutar, I. phase variables is used to study a multifrequency system with linearly transformed arguments on the interval [0, L]. Contrary to multifrequency systems in the standard form, we consider systems of equations, in which the speed of amplitude and phase variables can depend on a small parameter to various degrees. Existence and uniqueness of the solution is proven under the unique and existence condition of the averaged problem. An estimate of the averaging method which clearly depends on small parameters is found out. Initial and multipoint conditions for the solutions are considered. The results are illustrated by examples.

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Averaging in a Generalised Multifrequency System with a Delay

  • 章节

  • 发表日期：

    2025年

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  • Yaroslav Bihun,
  • Roman Petryshyn,
  • Ihor Skutar

摘要

The method of averaging byBihun, Y.Petryshyn, R.Skutar, I. phase variables is used to study a multifrequency system with linearly transformed arguments on the interval [0, L]. Contrary to multifrequency systems in the standard form, we consider systems of equations, in which the speed of amplitude and phase variables can depend on a small parameter to various degrees. Existence and uniqueness of the solution is proven under the unique and existence condition of the averaged problem. An estimate of the averaging method which clearly depends on small parameters is found out. Initial and multipoint conditions for the solutions are considered. The results are illustrated by examples.