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.
Editor-in-Chief
Dr. Vesselin Vatchev, USA
Honorary and Advisory Editors
Catherine Bandle, Basel, Switzerland
Jiguang Bao, Beijing, China
Avner Friedman, Columbus, Ohio, USA
Manuel del Pino, Bath, UK, and Santiago, Chile
Mikio Kato, Nagano, Japan
Guozhen Lu, Storrs, CT, USA
Wojciech Kryszewski, Lodz University of Technology, Poland
Vicentiu D. Radulescu, Kraków, Poland
Simeon Reich, Haifa, Israel
Please submit book proposals to Jürgen Appell.
Titles in planning include
Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy–Leray Potential (2020)
Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)
Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)
"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
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.
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.
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. These assumption implies the development of the theory of measure of noncompactness and the construction of a degree theory for condensing mapping.
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.
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
Über den Autor
Prof. Pietro Zecca, Dipartimento di Energetica, Universit¿egli studi di Firenze, Italy.nProf. Mikhail Kamenski¿University of Voronezh, Russia and Universit¿e Rouen, France.nValeri Obukhovski¿Universit¿i Firenze, Italy. nn
Inhaltsverzeichnis
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
Klappentext
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.
