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2008 Generalized Solutions of Functional Differential Inclusions
Anna Machina, Aleksander Bulgakov, Anna Grigorenko
Abstr. Appl. Anal. 2008: 1-35 (2008). DOI: 10.1155/2008/829701

Abstract

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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Anna Machina. Aleksander Bulgakov. Anna Grigorenko. "Generalized Solutions of Functional Differential Inclusions." Abstr. Appl. Anal. 2008 1 - 35, 2008. https://doi.org/10.1155/2008/829701

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1149.34037
MathSciNet: MR2377427
Digital Object Identifier: 10.1155/2008/829701

Rights: Copyright © 2008 Hindawi

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