Abstract and Applied Analysis
Volume 2003 (2003), Issue 13, Pages 769-784
On boundary value problems for degenerate differential inclusions in Banach spaces
1Department of Mathematics, Voronezh University, Voronezh 394 693, Russia
2Dipartimento di Energetica “Sergio Stecco”, Università degli Studi di Firenze, Firenze 50139, Italy
Received 21 December 2002
Copyright © 2003 Valeri Obukhovskii and Pietro Zecca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. Some particular cases including periodic problems are considered.