Abstract and Applied Analysis

Generalized Solutions of Functional Differential Inclusions

Anna Machina, Aleksander Bulgakov, and Anna Grigorenko

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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.

Article information

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

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969142

Digital Object Identifier
doi:10.1155/2008/829701

Mathematical Reviews number (MathSciNet)
MR2377427

Zentralblatt MATH identifier
1149.34037

Citation

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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