Generalized solutions of functional differential inclusions
type: Item
instance of: scholarly article
title: Generalized solutions of functional differential inclusions
zbMATH Open document ID: 1149.34037
DOI: 10.1155/2008/829701
author: A. Machina
author: Aleksander Bulgakov
author: Anna Grigorenko
published in: Abstract and Applied Analysis
publication date: 2008-08-19T00:00:00Z
full work available at URL: https://eudml.org/doc/54691
review text: Summary: 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.
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 5313160
Wikidata QID: Q58643835
MaRDI profile type: Publication
OpenAlex ID: W2010630995
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description: scientific article; zbMATH DE number 5313160