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Topics in Nonlinear Functional Analysis
Louis Nirenberg, New York University-Courant Institute of Mathematical Sciences, NY
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University.
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Courant Lecture Notes
2001; 145 pp; softcover
Volume: 6
ISBN-10: 0-8218-2819-3
ISBN-13: 978-0-8218-2819-9
List Price: US$26
Member Price: US$20.80
Order Code: CLN/6
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Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book 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

"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

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

Table of Contents

  • Topological approach: Finite dimensions
  • Topological degree in Banach space
  • Bifurcation theory
  • Further topological methods
  • Monotone operators and the min-max theorem
  • Generalized implicit function theorems
  • Bibliography
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