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Nonlinear analysis is a remarkable mixture of topology, analysis and applied mathematics. Mathematicians have good reason to become acquainted with this important, rapidly developing subject. But it is a BIG subject. You can feel it: just hold Eberhard Zeidler's Nonlinear Functional Analysis and Its Applications I: Fixed Point Theorems [Z} in your hand. It's heavy, as a 900 page book must be. Yet this is no encyclopedia; the preface accurately describes the " ... very careful selection of material ... " it contains. And what you are holding is only Part I of a five-part work. So how do you get started learning nonlinear analysis? Zeidler's book has a first page, and some people are quite comfortable beginning right there. For an alternative, the bibliography in [Z], which is 42 pages long, contains exposition as well as research results: monographs that explain portions of the subject to a variety of audiences. In particular, [D} covers much of the material of Zeidler's book. What makes this book different? The answer is in three parts: this book is (i) topological (ii) goal-oriented and (iii) a model of its subject.
Reviews / Votes
"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory... reading is fluid and very pleasant... style is informal but far from being imprecise."
- Mathematical Reviews (Review of the first edition)
"For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."
- Monatshefte für Mathematik
"Written by an expert in fixed point theory who is well aware of the important applications of this area to nonlinear analysis and differential equations, the first edition of this book has been very well received, and has helped both topologists in learning nonlinear analysis and analysts in appreciating topological fixed point theory. The second edition has kept the freshness and clarity of style of the first one. The new version remains more than even an excellent introduction to the sue of topological techniques in dealing with nonlinear problems."
---Mathematical Society
Series
Language
Place of publication
Publishing group
Target group
Professional and scholarly
Illustrations
File size
ISBN-13
978-1-4757-1209-4 (9781475712094)
DOI
10.1007/978-1-4757-1209-4
Schweitzer Classification
I: Fixed Point Existence Theory.- 1. The Topological Point of View.- 2. Ascoli-Arzela Theory.- 3. Brouwer Fixed Point Theory.- 4. Schauder Fixed Point Theory.- 5. Equilibrium Heat Distribution.- 6. Generalized Bernstein Theory.- II: Degree and Bifurcation.- 7. Some Topological Background.- 8. Brouwer Degree.- 9. Leray-Schauder Degree.- 10. Properties of the Leray-Schauder Degree.- 11. A Separation Theorem.- 12. Compact Linear Operators.- 13. The Degree Calculation.- 14. The Krasnoselskii-Rabinowitz Bifurcation Theorem.- 15. Nonlinear Sturm-Liouville Theory.- 16. Euler Buckling.- Appendices.- A. Singular Homology.- B. Additivity and Product Properties.- References.
