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Bifurcation Theory

An Introduction with Applications to Partial Differential Equations

  • Hansjörg Kielhöfer

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. Hansjörg Kielhöfer
    Pages 3-6
  3. Hansjörg Kielhöfer
    Pages 7-193
  4. Hansjörg Kielhöfer
    Pages 195-240
  5. Hansjörg Kielhöfer
    Pages 241-386
  6. Back Matter
    Pages 387-398

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.

 

The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.

Keywords

Bifurcation Theory Hopf Bifurcation Leray Schauder Degree partial differential equations

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0502-3
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-0501-6
  • Online ISBN 978-1-4614-0502-3
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site