Multiplicity Theorems for Frechet Manifolds

TL;DR

This paper establishes multiplicity theorems for invariant functionals on Frechet manifolds, providing lower bounds on the number of critical points using topological methods like Lusternik-Schnirelmann category.

Contribution

It extends multiplicity results to Keller $ C_c^1 $-functionals on Frechet spaces and manifolds, incorporating group invariance and topological tools.

Findings

Proves lower bounds on critical points for invariant functionals

Applies Lusternik-Schnirelmann category to infinite-dimensional settings

Extends classical multiplicity theorems to Frechet manifolds

Abstract

We prove multiplicity theorems for Keller $ C_c^1 $-functionals on Frechet spaces and Finsler manifolds which are invariant under the action of a discrete subgroup. For such functionals, we evaluate the minimal number of critical points by applying the Lusternik-Schnirelmann category.