Averaging of Set Integrodifferential Equations

The averaging method is one of the most used tools to study dynamical systems. With the development of the theory of differential inclusions, a respective generalization of the averaging method followed the steps outlined in the theory of differential equations. Presently, it has been successfully applied to a wide range of problems involving differential inclusions, simplifying the study of the systems under consideration. In this work, the main development trends and methods in the application of the averaging method to the study of stability and optimality of solutions to differential inclusions are surveyed. A detailed list of references is given and some examples of applications are presented.

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Conditions for the Existence of Local Solutions of Set-Valued Differential Equations with Generalized Derivative

Plotnikov

Skripnik

2014

Ukr Math J

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Averaging of Set Integrodifferential Equations

Abstract: In this article we prove the substantiation of the method of averaging for the set integrodifferential equations with small parameter. Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging.

Cited by 3 publications

References 29 publications

Three-Step Averaging Scheme for Set-Valued Differential Equations with Generalized Derivative

Three-Step Averaging Scheme for Set-Valued Differential Equations with Generalized Derivative

Stability and Optimality of Solutions to Differential Inclusions via Averaging Method

Conditions for the Existence of Local Solutions of Set-Valued Differential Equations with Generalized Derivative

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