Abstract and Applied Analysis

Generalized Solutions of Functional Differential Inclusions

Anna Machina, Aleksander Bulgakov, and Anna Grigorenko

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We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable in L 1 n [ a , b ] . The concept of the decomposable hull of a set is introduced. Using this concept, we define a generalized solution of such a problem and study its properties. We have proven that standard results on local existence and continuation of a generalized solution remain true. The question on the estimation of a generalized solution with respect to a given absolutely continuous function is studied. The density principle is proven for the generalized solutions. Asymptotic properties of the set of generalized approximate solutions are studied.

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Abstr. Appl. Anal., Volume 2008 (2008), Article ID 829701, 35 pages.

First available in Project Euclid: 9 September 2008

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Machina, Anna; Bulgakov, Aleksander; Grigorenko, Anna. Generalized Solutions of Functional Differential Inclusions. Abstr. Appl. Anal. 2008 (2008), Article ID 829701, 35 pages. doi:10.1155/2008/829701. https://projecteuclid.org/euclid.aaa/1220969142

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