Generalized Solutions of Functional Differential Inclusions
Anna Machina, Aleksander Bulgakov, and Anna Grigorenko
Source: Abstr. Appl. Anal. Volume 2008
(2008), Article ID
829701, 35 pages.
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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Permanent link to this document: http://projecteuclid.org/euclid.aaa/1220969142
Digital Object Identifier: doi:10.1155/2008/829701
Mathematical Reviews number (MathSciNet): MR2377427
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