A Topological Introduction to Nonlinear Analysis / Edition 2

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"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." -review of the first edition. New to this edition: additional applications of the theory and techniques, as well as several new proofs. This book is ideal for self-study for mathematicians and students interested in geometric and algebraic topology, functional analysis, differential equations, and applied mathematics.

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Editorial Reviews

From the Publisher
"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

Based on ideas from several branches of topology, and illustrated by numerous figures that attest to the geometric nature of the exposition, provides mathematically sophisticated readers with an understanding of the mathematics of the nonlinear phenomena that characterize the real world. A classical example is given in the differential equation problem that models the maximum weight that a column can support without buckling. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780817632588
  • Publisher: Birkhauser Verlag
  • Publication date: 12/12/2003
  • Edition description: 2nd ed. 2004
  • Edition number: 2
  • Pages: 184
  • Product dimensions: 0.42 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface.- Part I: Fixed Point Existence Theory.- The Topological Point of View.- Ascoli-Arzela Theory.- Brouwer Fixed Point Theory.- Schauder Fixed Point Theory.- The Forced Pendulum.- Equilibrium Heat Distribution.- Generalized Bernstein Theory.- Part II: Degree Theory.- Brouwer Degree.- Leray-Schauder Degree.- Properties of the Leray-Schauder Degree.- The Mawhin Operator.- The Pendulum Swings Back.- Part III: Bifurcation Theory.- A Separation Theorem.- Compact Linear Operators.- The Degree Calculation.- The Krasnoselskii-Rabinowitz Bifurcation Theorem.- Nonlinear Sturm-Liouville Theory.- Euler Buckling.- Part IV: Appendices.- Singular Homology.- Additivity and Product Properties.- Bounded Linear Transformations.- References.- Index

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