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Bifurcation Theory

An Introduction with Applications to PDEs

  • Hansjörg Kielhöfer

Part of the Applied Mathematical Sciences book series (AMS, volume 156)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Hansjörg Kielhöfer
    Pages 1-4
  3. Hansjörg Kielhöfer
    Pages 5-174
  4. Hansjörg Kielhöfer
    Pages 175-218
  5. Hansjörg Kielhöfer
    Pages 219-334
  6. Back Matter
    Pages 335-348

About this book

Introduction

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.

Keywords

Vibration bifurcation bifurcation theory operator partial differential equation stability

Authors and affiliations

  • Hansjörg Kielhöfer
    • 1
  1. 1.Institute for MathematicsUniversity of AugsburgAugsburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/b97365
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-9380-1
  • Online ISBN 978-0-387-21633-1
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site