**Courant Lecture Notes**

Volume: 6;
2001;
145 pp;
Softcover

MSC: Primary 46;

Print ISBN: 978-0-8218-2819-9

Product Code: CLN/6

List Price: $28.00

AMS Member Price: $22.40

MAA Member Price: $25.20

**Electronic ISBN: 978-1-4704-3108-2
Product Code: CLN/6.E**

List Price: $28.00

AMS Member Price: $22.40

MAA Member Price: $25.20

# Topics in Nonlinear Functional Analysis

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*Louis Nirenberg*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

Since its first appearance as a set of lecture notes published by the Courant
Institute in 1974, this book has served as an introduction to various subjects in
nonlinear functional analysis. The current edition is a reprint of these notes,
with added bibliographic references.

Topological and analytic methods are developed for treating nonlinear ordinary
and partial differential equations. The first two chapters of the book
introduce the notion of topological degree and develop its basic properties.
These properties are used in later chapters in the discussion of bifurcation
theory (the possible branching of solutions as parameters vary), including the
proof of Rabinowitz's global bifurcation theorem. Stability of the branches is
also studied. The book concludes with a presentation of some generalized
implicit function theorems of Nash-Moser type with applications to
Kolmogorov-Arnold-Moser theory and to conjugacy problems.

After more than 20 years, this book continues to be an excellent graduate
level textbook and a useful supplementary course text.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Readership

Graduate students and research mathematicians interested in functional analysis.

#### Reviews & Endorsements

This is the second edition of the well-known and remarkable book on nonlinear analysis … The book is useful for all specialists in nonlinear analysis, first for young mathematicians that, due to this book, can become acquainted with a series of fundamental and brilliant ideas and methods of nonlinear analysis.

-- Zentralblatt MATH

These lecture notes are extremely stimulating.

-- Zentralblatt MATH

[The book] is short, concise, and to the point, and the proofs are unusually elegant, always with a geometric flavor and the best available.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## Topics in Nonlinear Functional Analysis

- Cover Cover11
- General editor information iv5
- Title page v6
- Contents vii8
- Preface to the new edition ix10
- Preface xi12
- Topological approach: Finite dimensions 114
- Topological degree in Banach space 1932
- Bifurcation theory 3952
- Further topological methods 7184
- Monotone operators and the min-max theorem 93106
- Generalized implicit function theorems 107120
- Bibliography 143156
- Back Cover Back Cover1159