A primer of nonlinear analysis

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A primer of nonlinear analysis / Antonio Ambrosetti, Giovanni Prodi

版:

First paperback edition (with corrections)

資料種別:

図書

出版情報:

Cambridge : Cambridge University Press, 1995, c1993

形態:

viii, 171 p. ; 23 cm

シリーズ名:

Cambridge studies in advanced mathematics ; 34 <BA00109761>

著者名:

ISBN:

9780521485739 [0521485738]

書誌ID:

BA25825974

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Bibliography: p. [165]-169
Includes index

主題:

位相解析．関数解析

言語:

英語

目次情報:

Preface

Preliminaries and notation / 0：

Differential calculus / 1：

Frechet and Gateaux derivatives

Continuity and differentiability of Nemitski operators / 2：

Higher derivatives / 3：

Partial derivatives, Taylor's formula / 4：

Local inversion theorems

The Local Inversion Theorem

The Implicit Function Theorem

A stability property of orbits

Global inversion theorems

The Global Inversion Theorem

Global inversion with singularities

Appendix

Semilinear Dirichlet problems

Problems at resonance

Problems with asymmetric nonlinearities

Bifurcation results / 5：

Introduction

Some elementary examples

The Lyapunov-Schmidt reduction

Bifurcation from the simple eigenvalue

A bifurcation theorem from a multiple eigenvalue

Bifurcation problems / 6：

The rotating heavy string

The Benard problem

Small oscillations for second-order dynamical systems

Water waves

Periodic solutions of a semilinear hyperbolic equation

Bifurcation of periodic solutions / 7：

The Hopf bifurcation

Nonlinear oscillations of autonomous systems

The Lyapunov Centre Theorem

The restricted three-body problem

Problems

Bibliography

Index

Preface

Preliminaries and notation / 0：

Differential calculus / 1：

Frechet and Gateaux derivatives

Continuity and differentiability of Nemitski operators / 2：

Higher derivatives / 3：

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