Condensing multivalued maps and semilinear differential inclusions in Banach spaces / Mikhail Kamenskii, Valeri Obukhovskii, Pietro Zecca.

Format:

Book

Author/Creator:

Kamenskii, Mikhail, 1950-

Contributor:

Obukhovskii, Valeri, 1947-

Zecca, P. (Pietro)

Series:

De Gruyter series in nonlinear analysis and applications ; 0941-813X 7.

De Gruyter series in nonlinear analysis and applications, 0941-813X ; 7

Language:

English

Subjects (All):

Set-valued maps.

Differential inclusions.

Banach spaces.

Physical Description:

xi, 231 p.

Edition:

Reprint 2011

Place of Publication:

Berlin ; New York : W. de Gruyter, 2001.

Language Note:

English

Summary:

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.

Contents:

Front matter

Introduction

Contents

Chapter 1. Multivalued maps: general properties

Chapter 2. Measures of noncompactness and condensing multimaps

Chapter 3. Topological degree theory for condensing multifields

Chapter 4. Semigroups and measures of noncompactness

Chapter 5. Semilinear differential inclusions: initial problem

Chapter 6. Semilinear inclusions: periodic problems

Bibliographic notes

Bibliography

Index

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. [213]-228) and index.

ISBN:

9783110870893

3110870894

OCLC:

979748143