Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.

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.

Auteur

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.

Résumé

"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

Contenu
Multivalued maps: general properties · Measures of noncompactness and condensing multimaps · Topological degree theory for condensing multifields · Semigroups and measures of noncompactness · Semilinear differential inclusions: initial problem · Semilinear inclusions: periodic problems Bibliographic notes