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Softcover ISBN:  9780821828199 
Product Code:  CLN/6 
List Price:  $30.00 
MAA Member Price:  $27.00 
AMS Member Price:  $24.00 
eBook ISBN:  9781470431082 
Product Code:  CLN/6.E 
List Price:  $28.00 
MAA Member Price:  $25.20 
AMS Member Price:  $22.40 
Softcover ISBN:  9780821828199 
eBook ISBN:  9781470431082 
Product Code:  CLN/6.B 
List Price:  $58.00$44.00 
MAA Member Price:  $52.20$39.60 
AMS Member Price:  $46.40$35.20 

Book DetailsCourant Lecture NotesVolume: 6; 2001; 145 ppMSC: Primary 46;
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 NashMoser type with applications to KolmogorovArnoldMoser 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.ReadershipGraduate students and research mathematicians interested in functional analysis.

Table of Contents

Chapters

Chapter 1. Topological approach: Finite dimensions

Chapter 2. Topological degree in Banach space

Chapter 3. Bifurcation theory

Chapter 4. Further topological methods

Chapter 5. Monotone operators and the minmax theorem

Chapter 6. Generalized implicit function theorems


Reviews

This is the second edition of the wellknown 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 
From reviews for the First Edition: 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


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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 NashMoser type with applications to KolmogorovArnoldMoser 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.
Graduate students and research mathematicians interested in functional analysis.

Chapters

Chapter 1. Topological approach: Finite dimensions

Chapter 2. Topological degree in Banach space

Chapter 3. Bifurcation theory

Chapter 4. Further topological methods

Chapter 5. Monotone operators and the minmax theorem

Chapter 6. Generalized implicit function theorems

This is the second edition of the wellknown 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 
From reviews for the First Edition: 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