This article is cited in 2 papers

The functional differential inclusions with impulses and with the right-hand side not necessarily convex-valued with respect to switching

A. I. Bulgakov, O. V. Filippova

Tambov State University, ul. Internatsional’naya, 33, Tambov, 392000, Russia

Abstract: The Cauchy problem for the functional differential inclusion with Volterra's multivalued map not necessarily convex-valued with respect to switching and with impulses is considered. For this problem, the definition of a generalized solution is introduced, and the questions of existence and extendibility of generalized solutions are studied. Notions of a near-realization and realization of the distance to an arbitrary summable function by the set of generalized solutions are formulated. For a set of generalized solutions of functional differential inclusions with impulses and with multivalued map not necessarily convex-valued with respect to switching, estimations are found similar to A. F. Filippov's estimations. The generalized principle of density is proved.

Keywords: functional differential inclusion, convex-valued with respect to switching, generalized solution, the near-realization and realization of the distance to a given summable function by the set of generalized solutions, a-priori boundedness.

UDC: 517.965, 517.929.7

MSC: 34K15

Received: 01.02.2014

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