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

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

Series:De Gruyter Series in Nonlinear Analysis and Applications 7

    149,95 € / $210.00 / £136.50*

    eBook (PDF)
    Reprint 2011
    Publication Date:
    July 2011
    Copyright year:
    2001
    ISBN
    978-3-11-087089-3
    See all formats and pricing

    Overview

    Aims and Scope

    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.

    Details

    23.0 x 15.5 cm
    xi, 231 pages
    Language:
    English
    Keyword(s):

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    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

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