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Lecture Notes in Mathematics

Topological Methods for Variational Problems with Symmetries

Authors: Bartsch, Thomas

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About this book

Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $29.99
price for USA in USD
  • ISBN 978-3-540-48099-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA in USD
  • ISBN 978-3-540-57378-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topological Methods for Variational Problems with Symmetries
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1560
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-48099-0
DOI
10.1007/BFb0073859
Softcover ISBN
978-3-540-57378-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 158
Topics

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