Bifurcation Theory An Introduction With Applications

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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.

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Applied Mathematical Sciences Volume 156 Editors S.S. Antman J.E. Marsden L. Sirovich Advisors J.K. Hale P. Holmes J. Keener J. Keller B.J. Matkowsky A. Mielke C.S. Peskin K.R. Sreenivasan Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo Hansjo¨rg Kielho¨fer Bifurcation Theory An Introduction with Applications to PDEs With 38 Figures Springer Hansjo¨rg Kielho¨fer Institute for Mathematics University of Augsburg Universita¨tsstrasse 14, Raum 2011 D-86135 Augsburg Germany [email protected] Editors: S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA [email protected] J.E. Marsden Cont
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