Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces (De Gruyter Series in Nonlinear Analysis & Applications): 7 - Hardcover

Kamenskii, Mikhail I.; Obukhovskii, Valeri V.; Zecca, Pietro

Hardcover

ISBN 10: 3110169894 ISBN 13: 9783110169898

Publisher: De Gruyter, 2001

Synopsis

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications do not suppose neither convexity of the map or compactness of the multi-operators. These assumption implies the development of the theory of measure of noncompactness and the construction of a degree theory for condensing mapping. Of particular interest is the approach to the case when the linear part is a generator of a condensing, strongly continuous semigroup. In this context, the existence of solutions for the Cauchy and periodic problems are proved as well as the topological properties of the solution sets. Examples of applications to the control of transmission line and to hybrid systems are presented.

About this title

About the Author

Prof. Pietro Zecca, Dipartimento di Energetica, Università degli studi di Firenze, Italy.
Prof. Mikhail Kamenskiì, University of Voronezh, Russia and Université de Rouen, France.
Valeri Obukhovskiì, Università di Firenze, Italy.

Edition details

• Publisher: De Gruyter
• Publication date: 2001
• Language: English
• ISBN 10: 3110169894
• ISBN 13: 9783110169898
• Binding: Hardcover
• Number of pages: 242