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A Primer of Nonlinear Analysis : Cambridge Studies in Advanced Mathematics - Antonio Ambrosetti

A Primer of Nonlinear Analysis

Cambridge Studies in Advanced Mathematics

By: Antonio Ambrosetti, Giovanni Prodi, B. Bollobas (Editor), W. Fulton (Editor), A. Katok (Editor)

Paperback Published: 8th May 1995
ISBN: 9780521485739
Number Of Pages: 180

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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 differential 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.

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

Prefacep. vii
Preliminaries and notationp. 1
Differential calculusp. 9
Frechet and Gateaux derivativesp. 9
Continuity and differentiability of Nemitski operatorsp. 15
Higher derivativesp. 23
Partial derivatives, Taylor's formulap. 26
Local inversion theoremsp. 30
The Local Inversion Theoremp. 30
The Implicit Function Theoremp. 36
A stability property of orbitsp. 38
Global inversion theoremsp. 45
The Global Inversion Theoremp. 45
Global inversion with singularitiesp. 55
Appendixp. 60
Semilinear Dirichlet problemsp. 61
Problems at resonancep. 62
Problems with asymmetric nonlinearitiesp. 71
Bifurcation resultsp. 79
Introductionp. 79
Some elementary examplesp. 82
The Lyapunov-Schmidt reductionp. 89
Bifurcation from the simple eigenvaluep. 91
A bifurcation theorem from a multiple eigenvaluep. 101
Appendixp. 104
Bifurcation problemsp. 107
The rotating heavy stringp. 107
The Benard problemp. 112
Small oscillations for second-order dynamical systemsp. 119
Water wavesp. 123
Periodic solutions of a semilinear hyperbolic equationp. 130
Bifurcation of periodic solutionsp. 136
The Hopf bifurcationp. 136
Nonlinear oscillations of autonomous systemsp. 139
The Lyapunov Centre Theoremp. 145
The restricted three-body problemp. 153
Problemsp. 160
Bibliographyp. 165
Indexp. 170
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521485739
ISBN-10: 0521485738
Series: Cambridge Studies in Advanced Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 180
Published: 8th May 1995
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.11 x 15.7  x 1.25
Weight (kg): 0.29

Earn 126 Qantas Points
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