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Implicit forms of recording and continuous approximations of discontinuos systems


The method of representation of the differential equations with a discontinuous right-hand part in the implicit form is investigated. The method will be coordinated to known approaches, such as the convex definition in sense of Filippov, a method of equivalent control. Within the framework of conditions of monotony the implicit method allows to receive one-digit equations of movement of discontinuous systems, in particular - the equations of sliding modes. Continuous approximations of Yosida for explosive systems and estimations for exact and approximating solutions are considered. The same questions for delay differential equations are stuied.


differential equations with discontinuous right-hand part; right-hand condition of Lipschitz; sliding mode; approximation of Yosida; delay

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