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Bifurcation Theory

An Introduction with Applications to PDEs

  • Textbook
  • © 2004

Overview

Authors:
  1. Hansjörg Kielhöfer

    1. Institute for Mathematics, University of Augsburg, Augsburg, Germany

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction

    • Hansjörg Kielhöfer
    Pages 1-4

  3. Local Theory

    • Hansjörg Kielhöfer
    Pages 5-174

  4. Global Theory

    • Hansjörg Kielhöfer
    Pages 175-218

  5. Applications

    • Hansjörg Kielhöfer
    Pages 219-334

  6. Back Matter

    Pages 335-348
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Keywords

About this book

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.

Reviews

From the reviews:

"This unified exposition of the single-parameter bifurcation response of an operator on infinite dimensional space is organized into three sections … . The book is very useful as a reference because it collects and organizes the bifurcation analysis of infinite-dimensional operators. It could also be used as a text in an advanced course on bifurcation theory with an emphasis on partial differential equations." (HW Haslach, Applied Mechanics Reviews, Vol. 57 (5), September, 2004)

Authors and Affiliations

  • Institute for Mathematics, University of Augsburg, Augsburg, Germany

    Hansjörg Kielhöfer

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