Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

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

Published by De Gruyter 2001

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

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

Volume 7 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110870893

Overview
Contents

About this book

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.

Author / Editor information

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.

Reviews

"On the whole, the authors have done an impressive job in presenting material from at least three different areas on not much more than 200 pages. The style is clear, and the presentation is always reliable, leading the reader from first principles to the present state of the art, including a lot of new results." Mathematical Reviews

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
Introduction Requires Authentication Unlicensed Licensed Download PDF	V
Contents Requires Authentication Unlicensed Licensed Download PDF	IX
Chapter 1. Multivalued maps: general properties Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Measures of noncompactness and condensing multimaps Requires Authentication Unlicensed Licensed Download PDF	33
Chapter 3. Topological degree theory for condensing multifields Requires Authentication Unlicensed Licensed Download PDF	49
Chapter 4. Semigroups and measures of noncompactness Requires Authentication Unlicensed Licensed Download PDF	99
Chapter 5. Semilinear differential inclusions: initial problem Requires Authentication Unlicensed Licensed Download PDF	122
Chapter 6. Semilinear inclusions: periodic problems Requires Authentication Unlicensed Licensed Download PDF	175
Bibliographic notes Requires Authentication Unlicensed Licensed Download PDF	211
Bibliography Requires Authentication Unlicensed Licensed Download PDF	213
Index Requires Authentication Unlicensed Licensed Download PDF	229

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: Reprint 2011
Pages
- Front matter: 11
- Main content: 231
Keywords: Banach-Raum; Mengenwertige Abbildung; Differentialinklusion

eBook

Published: July 20, 2011
ISBN: 9783110870893

Hardcover

Published: May 15, 2001
ISBN: 9783110169898