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Brouwer Degree

The Core of Nonlinear Analysis

  • Book
  • © 2021

Overview

Authors:
  1. George Dinca

    1. Faculty of Mathematics & Computer Science, University of Bucharest, Bucharest, Romania

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  2. Jean Mawhin

    1. IRMP, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

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    You can also search for this author in PubMed   Google Scholar

  • Explores the Brouwer degree and its continuing impact on the development of nonlinear analysis
  • Uses an analytical approach with the language of differential forms to introduce the Brouwer degree with simplicity and clear motivation
  • Presents a broad view of the topic, including a wide variety of applications as well as numerous historical notes

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 95)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xix
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  2. The Kronecker Index and the Brouwer Degree

    • George Dinca, Jean Mawhin
    Pages 1-76

  3. Continuation, Existence and Bifurcation

    • George Dinca, Jean Mawhin
    Pages 77-133

  4. Infinite-Dimensional Problems

    • George Dinca, Jean Mawhin
    Pages 135-183

  5. Difference Equations

    • George Dinca, Jean Mawhin
    Pages 185-222

  6. Periodic Solutions of Differential Systems

    • George Dinca, Jean Mawhin
    Pages 223-261

  7. Two-Dimensional Problems

    • George Dinca, Jean Mawhin
    Pages 263-324

  8. The Degree of Some Classes of Mappings

    • George Dinca, Jean Mawhin
    Pages 325-389

  9. History of the Brouwer Fixed Point Theorem

    • George Dinca, Jean Mawhin
    Pages 391-412

  10. Back Matter

    Pages 413-447
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Keywords

About this book

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.

Authors and Affiliations

  • Faculty of Mathematics & Computer Science, University of Bucharest, Bucharest, Romania

    George Dinca

  • IRMP, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean Mawhin

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