A Primer of Nonlinear Analysis

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Paperback | 8 May 1995

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180 Pages

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22.86 x 15.24 x 1.04

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This is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two parts; the first deals with the geometry of Banach spaces and includes a discussion of local and global inversion theorems for differentiable mappings. In the second part, the authors are more concerned with bifurcation theory, including the Hopf bifurcation. They include plenty of motivational and illustrative applications, which indeed provide much of the justification of nonlinear analysis. In particular, they discuss bifurcation problems arising from such areas as mechanics and fluid dynamics. The book is intended to accompany upper division courses for students of pure and applied mathematics and physics; exercises are consequently included.

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'There's no more economical or lucid introduction to the subject than this great little book.' The Mathematical Intelligencer

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Preface	p. vii
Preliminaries and notation	p. 1
Differential calculus	p. 9
Frechet and Gateaux derivatives	p. 9
Continuity and differentiability of Nemitski operators	p. 15
Higher derivatives	p. 23
Partial derivatives, Taylor's formula	p. 26
Local inversion theorems	p. 30
The Local Inversion Theorem	p. 30
The Implicit Function Theorem	p. 36
A stability property of orbits	p. 38
Global inversion theorems	p. 45
The Global Inversion Theorem	p. 45
Global inversion with singularities	p. 55
Appendix	p. 60
Semilinear Dirichlet problems	p. 61
Problems at resonance	p. 62
Problems with asymmetric nonlinearities	p. 71
Bifurcation results	p. 79
Introduction	p. 79
Some elementary examples	p. 82
The Lyapunov-Schmidt reduction	p. 89
Bifurcation from the simple eigenvalue	p. 91
A bifurcation theorem from a multiple eigenvalue	p. 101
Appendix	p. 104
Bifurcation problems	p. 107
The rotating heavy string	p. 107
The Benard problem	p. 112
Small oscillations for second-order dynamical systems	p. 119
Water waves	p. 123
Periodic solutions of a semilinear hyperbolic equation	p. 130
Bifurcation of periodic solutions	p. 136
The Hopf bifurcation	p. 136
Nonlinear oscillations of autonomous systems	p. 139
The Lyapunov Centre Theorem	p. 145
The restricted three-body problem	p. 153
Problems	p. 160
Bibliography	p. 165
Index	p. 170
Table of Contents provided by Syndetics. All Rights Reserved.

A Primer of Nonlinear Analysis

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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