Brouwer Degree - George Dinca, Jean Mawhin

Brouwer Degree

The Core of Nonlinear Analysis
Buch | Softcover
XIX, 447 Seiten
2022 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-63232-8 (ISBN)
139,09 inkl. MwSt
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.

The Kronecker Index and the Brouwer Degree.- Continuation, Existence, and Bifurcation.- Infinite-Dimensional Problems.- Difference Equations.- Periodic Solutions of Differential Systems.- Two-Dimensional Problems.- The Degree of Some Classes of Mappings.- History of Brouwer Fixed Point Theorem.

Erscheinungsdatum
Reihe/Serie Progress in Nonlinear Differential Equations and Their Applications
Zusatzinfo XIX, 447 p. 2 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 712 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
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 3-030-63232-6 / 3030632326
ISBN-13 978-3-030-63232-8 / 9783030632328
Zustand Neuware
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