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Topics in Nonlinear Functional Analysis
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Topics in Nonlinear Functional Analysis

Topics in Nonlinear Functional Analysis

Louis Nirenberg

144 pages, parution le 17/12/2001

Résumé

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 copublished with the Courant Institute of Mathematical Sciences at New York University

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

Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Louis Nirenberg
Parution 17/12/2001
Nb. de pages 144
Format 17,6 x 25,3
Couverture Broché
Poids 250g
Intérieur Noir et Blanc
EAN13 9780821828199
ISBN13 978-0-8218-2819-9

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