Applied Mathematical Sciences

Bifurcation Theory

An Introduction with Applications to Partial Differential Equations

Authors: Kielhöfer, Hansjörg

  • Gives a unified presentation in an abstract setting
  • Two new sections along with many revisions
  • More references included
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Hardcover $79.99
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  • ISBN 978-1-4614-0501-6
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  • ISBN 978-1-4939-0140-1
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About this Textbook

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.

 

 

About the authors

Hansjörg Kielhöfer is a Professor at the University of Augsburg, Germany.

Reviews

From the reviews of the second edition:

“This book is a valuable resource for mathematicians working in the areas of Nonlinear Analysis and/or Differential Equations. … This book is intended for advanced graduate students, for specialists in Bifurcation Theory and for researchers in related areas willing to master the subject. … this is a great reference book on the subject of Bifurcations.” (Florin Catrina, MAA Reviews, January, 2013)

“The volume under review gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, in relation with some new results and relevant applications to partial differential equations. … The book is very well written and the many examples make it an excellent choice for a good course on bifurcation problems.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1230, 2012)


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Table of contents (4 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4614-0502-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4614-0501-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4939-0140-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Bifurcation Theory
Book Subtitle
An Introduction with Applications to Partial Differential Equations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
156
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-0502-3
DOI
10.1007/978-1-4614-0502-3
Hardcover ISBN
978-1-4614-0501-6
Softcover ISBN
978-1-4939-0140-1
Series ISSN
0066-5452
Edition Number
2
Number of Pages
VIII, 400
Topics