Topological Methods for Variational Problems with Symmetries

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.