Brouwer Degree (eBook)

The Core of Nonlinear Analysis

George Dinca, Jean Mawhin (Autoren)

eBook Download: PDF

2021 | 1st ed. 2021
XIX, 447 Seiten
Springer International Publishing (Verlag)
978-3-030-63230-4 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 11.5.2021
• Reihe/Serie: Progress in Nonlinear Differential Equations and Their Applications
• Reihe/Serie: Progress in Nonlinear Differential Equations and Their Applications
• Zusatzinfo: XIX, 447 p. 2 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: Bifurcation Brouwer degree • Brouwer Degree • Brouwer Degree difference equations • Brouwer Degree differential equations • Brouwer Degree Nonlinear Analysis • Brouwer fixed-point theorem • Continuation theorems • Kakutani fixed point theorem • KMM theorem • Kroenecker Index • Nash equilibrium non-cooperative game • Surjectivity Brouwer degree • Von Neumann minimax theorem
• ISBN-10: 3-030-63230-X / 303063230X
• ISBN-13: 978-3-030-63230-4 / 9783030632304