Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2008 (2008), Article ID 829701, 35 pages.
Generalized Solutions of Functional Differential Inclusions
We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable in . 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.
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 829701, 35 pages.
First available in Project Euclid: 9 September 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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