Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces (De Gruyter Series in Nonlinear Analysis and Applications, 7)

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

ISBN 10: 3110169894 / ISBN 13: 9783110169898

Published by De Gruyter, 2001

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Bibliographic Details

• Title: Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces (De Gruyter Series in Nonlinear Analysis and Applications, 7)
• Publisher: De Gruyter
• Publication Date: 2001
• Language: English
• ISBN 10: 3110169894
• ISBN 13: 9783110169898
• Binding: Hardcover
• Condition: New

About this title

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 the Author

Prof. Pietro Zecca, Dipartimento di Energetica, Universitą degli studi di Firenze, Italy. Prof. Mikhail Kamenskiģ, University of Voronezh, Russia and Université de Rouen, France. Valeri Obukhovskiģ, Universitą di Firenze, Italy.