A Topological Introduction to Nonlinear Analysis / Edition 2

A Topological Introduction to Nonlinear Analysis / Edition 2

by Robert F. Brown
     
 

ISBN-10: 0817632581

ISBN-13: 9780817632588

Pub. Date: 12/12/2003

Publisher: Birkhauser Verlag

"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)

Here is a book that will be a joy to the mathematician or graduate student of

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Overview

"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)

Here is a book that will be a joy to the mathematician or graduate student of mathematics—-or even the well-prepared undergraduate—-who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world.

New to the second edition: New chapters will supply additional applications of the theory and techniques presented in the book.

• Several new proofs, making the second edition more self-contained.

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Product Details

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

Table of Contents

Preface
Pt. IFixed Point Existence Theory
1The Topological Point of View3
2Ascoli-Arzela Theory9
3Brouwer Fixed Point Theory19
4Schauder Fixed Point Theory23
5The Forced Pendulum29
6Equilibrium Heat Distribution39
7Generalized Bernstein Theory45
Pt. IIDegree Theory
8Brouwer Degree51
9Properties of the Brouwer Degree55
10Leray-Schauder Degree63
11Properties of the Leray-Schauder Degree69
12The Mawhin Operator79
13The Pendulum Swings Back85
Pt. IIIBifurcation Theory
14A Separation Theorem95
15Compact Linear Operators99
16The Degree Calculation111
17The Krasnoselskii-Rabinowitz Bifurcation Theorem119
18Nonlinear Sturm-Liouville Theory133
19More Sturm-Liouville Theory143
20Euler Buckling155
Pt. IVAppendices
ASingular Homology163
BAdditivity and Product Properties169
CBounded Linear Transformations175
References181
Index183

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