A Topological Introduction to Nonlinear Analysis / Edition 1

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Overview

This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of non-linear analysis by a practicing topologist who has seen a clear path to understanding.
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Editorial Reviews

Booknews
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: 9780817637064
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 6/1/1996
  • Edition number: 1
  • Pages: 146

Table of Contents

Preface
Pt. I Fixed Point Existence Theory
1 The Topological Point of View 3
2 Ascoli-Arzela Theory 9
3 Brouwer Fixed Point Theory 19
4 Schauder Fixed Point Theory 23
5 The Forced Pendulum 29
6 Equilibrium Heat Distribution 39
7 Generalized Bernstein Theory 45
Pt. II Degree Theory
8 Brouwer Degree 51
9 Properties of the Brouwer Degree 55
10 Leray-Schauder Degree 63
11 Properties of the Leray-Schauder Degree 69
12 The Mawhin Operator 79
13 The Pendulum Swings Back 85
Pt. III Bifurcation Theory
14 A Separation Theorem 95
15 Compact Linear Operators 99
16 The Degree Calculation 111
17 The Krasnoselskii-Rabinowitz Bifurcation Theorem 119
18 Nonlinear Sturm-Liouville Theory 133
19 More Sturm-Liouville Theory 143
20 Euler Buckling 155
Pt. IV Appendices
A Singular Homology 163
B Additivity and Product Properties 169
C Bounded Linear Transformations 175
References 181
Index 183
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