Overview

-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.

Full Product Details

Author:   Robert F. Brown
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2nd ed. 2004
Dimensions:   Width: 15.50cm , Height: 1.00cm , Length: 23.50cm
Weight:   0.640kg
ISBN:  

9780817632588

ISBN 10:   0817632581
Pages:   184
Publication Date:   12 December 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Replaced By:   9783319117935
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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 The Forced Pendulum.- 6 Equilibrium Heat Distribution.- 7 Generalized Bernstein Theory.- II Degree Theory.- 8 Brouwer Degree.- 9 Properties of the Brouwer Degree.- 10 Leray-Schauder Degree.- 11 Properties of the Leray-Schauder Degree.- 12 The Mawhin Operator.- 13 The Pendulum Swings Back.- III Bifurcation Theory.- 14 A Separation Theorem.- 15 Compact Linear Operators.- 16 The Degree Calculation.- 17 The Krasnoselskii-Rabinowitz Bifurcation Theorem.- 18 Nonlinear Sturm-Liouville Theory.- 19 More Sturm-Liouville Theory.- 20 Euler Buckling.- IV Appendices.- A Singular Homology.- B Additivity and Product Properties.- C Bounded Linear Transformations.- C Bounded Linear Transformations.- References.

Reviews

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 fur 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

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. <p>- Mathematical Reviews (Review of the first edition) <p> 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. <p>- Monatshefte fA1/4r Mathematik <p> 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

Aus den Rezensionen zur 2. Auflage: ! Um auf nicht einmal 200 Seiten ein sinnvolles Bild des umfangreichen Gegenstandes zu zeichnen, muss namlich eine sehr selektive Stoffauswahl getroffen werden. Sehr wohl werden ... drei Anspruche erhoben, welchen das Buch auf sicherlich vorbildliche Weise gerecht wird ... Dies wird durch eine klare Gliederung in drei Teile und einen Anhang erreicht. ... Mit seinem ... verbalen und doch sehr prazisen Stil versteht es der Autor hervorragend, die entscheidenden Ideen zu vermitteln. ... Deshalb kann das Buch als Einfuhrung in den Gegenstand uneingeschrankt empfohlen werden ... (R. Winkler, in: IMN - Internationale Mathematische Nachrichten, 2005, Vol. 198, S. 33)

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