G. Gaeta
Counting symmetry breaking solutions to symmetric variational problems
(33K, Plain TeX)
ABSTRACT. By combining the Michel's geometric theory of symmetry breaking and classical
result from variational analysis, we obtain a lower bound on critical
points with
given symmetry $H \sse G$ of a potential symmetric under $G$. The result is
obtained
by applying Ljusternik-Schnirelman category in the group orbit space, and can be
extendeded along the same lines to more general situations.