Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces / / Mikhail I. Kamenskii, Valeri V. Obukhovskii, Pietro Zecca.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications
• VerfasserIn: Kamenskii, Mikhail I.,; Obukhovskii, Valeri V.,; Zecca, Pietro,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2001
• Year of Publication: 2011
• Edition: Reprint 2011
• Language: English
• Series: De Gruyter Series in Nonlinear Analysis and Applications , 7
• Physical Description: 1 online resource (231 p.)

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.

Table of Contents

Frontmatter -- 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