# Topological Methods for Variational Problems with Symmetries

Part of the Lecture Notes in Mathematics book series (LNM, volume 1560)

Part of the Lecture Notes in Mathematics book series (LNM, volume 1560)

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.

Algebraic topology Dynamical systems bifurcation theory critical point theory equivariant topology minimum variational problems

- DOI https://doi.org/10.1007/BFb0073859
- Copyright Information Springer-Verlag Berlin Heidelberg 1993
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-57378-4
- Online ISBN 978-3-540-48099-0
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- About this book