Authors:
- Gives a unified presentation in an abstract setting
- Two new sections along with many revisions
- More references included
Part of the book series: Applied Mathematical Sciences (AMS, volume 156)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
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.
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.
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)
Authors and Affiliations
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, Institute of Mathematics, University of Augsburg, Augsburg, Germany
Hansjörg Kielhöfer
About the author
Bibliographic Information
Book Title: Bifurcation Theory
Book Subtitle: An Introduction with Applications to Partial Differential Equations
Authors: Hansjörg Kielhöfer
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-1-4614-0502-3
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-1-4614-0501-6Published: 12 November 2011
Softcover ISBN: 978-1-4939-0140-1Published: 25 January 2014
eBook ISBN: 978-1-4614-0502-3Published: 13 November 2011
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 2
Number of Pages: VIII, 400
Topics: Partial Differential Equations, Dynamical Systems and Ergodic Theory, Applications of Mathematics, Theoretical and Applied Mechanics