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Brouwer Degree: The Core of Nonlinear Analysis: 95 (Progress in Nonlinear Differential Equations and Their Applications, 95) - Hardcover

Book 52 of 53: Progress in Nonlinear Differential Equations and Their Applications

Dinca, George; Mawhin, Jean

 
9783030632298: Brouwer Degree: The Core of Nonlinear Analysis: 95 (Progress in Nonlinear Differential Equations and Their Applications, 95)
Hardcover
ISBN 10: 3030632296 ISBN 13: 9783030632298
Publisher: Birkhäuser, 2021

Synopsis

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.

"synopsis" may belong to another edition of this title.

From the Back Cover

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.

"About this title" may belong to another edition of this title.

Publisher
Birkhäuser
Publication date
2021
Language
English
ISBN 10 
3030632296
ISBN 13 
9783030632298
Binding
Hardcover
Edition number
1
Number of pages
466