Brouwer Degree

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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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.

• Brouwer Degree
• Brouwer Degree Nonlinear Analysis
• Brouwer Degree differential equations
• Brouwer Degree difference equations
• Brouwer Fixed-Point Theorem
• Kroenecker Index
• KMM theorem
• Bifurcation Brouwer degree
• Continuation theorems
• Surjectivity Brouwer degree
• Kakutani fixed point theorem
• Von Neumann minimax theorem
• Nash equilibrium non-cooperative game

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

  George Dinca

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

  Jean Mawhin