Methods of Bifurcation Theory

  • Shui-Nee Chow
  • Jack K. Hale

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 251)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Shui-Nee Chow, Jack K. Hale
    Pages 1-18
  3. Shui-Nee Chow, Jack K. Hale
    Pages 19-88
  4. Shui-Nee Chow, Jack K. Hale
    Pages 89-114
  5. Shui-Nee Chow, Jack K. Hale
    Pages 115-167
  6. Shui-Nee Chow, Jack K. Hale
    Pages 168-214
  7. Shui-Nee Chow, Jack K. Hale
    Pages 215-243
  8. Shui-Nee Chow, Jack K. Hale
    Pages 244-283
  9. Shui-Nee Chow, Jack K. Hale
    Pages 284-310
  10. Shui-Nee Chow, Jack K. Hale
    Pages 311-348
  11. Shui-Nee Chow, Jack K. Hale
    Pages 349-367
  12. Shui-Nee Chow, Jack K. Hale
    Pages 368-400
  13. Shui-Nee Chow, Jack K. Hale
    Pages 401-442
  14. Shui-Nee Chow, Jack K. Hale
    Pages 443-466
  15. Shui-Nee Chow, Jack K. Hale
    Pages 467-490
  16. Back Matter
    Pages 491-518

About this book

Introduction

An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate­ rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.

Keywords

Differentialgleichung Eigenvalue Implicit function Nichtlineare Funktionalanalysis Verzweigung banach spaces bifurcation differential equation functional analysis integral manifold minimum ordinary differential equation sets stability

Authors and affiliations

  • Shui-Nee Chow
    • 1
  • Jack K. Hale
    • 2
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8159-4
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8161-7
  • Online ISBN 978-1-4613-8159-4
  • Series Print ISSN 0072-7830
  • About this book