Multiple critical points for indefinite functionals and applications (Q1293266)

The main purpose of this paper is to establish a multiplicity result of Ljusternik-Schnirelman type for ``saddle'' critical points of indefinite functionals which are defined on complete Riemann manifolds modelled on a Hilbert space. The proof relies on a min-max argument based on the classical Palais' Deformation Lemma. As an application of this abstract result, the authors show the existence of multiple timelike periodic trajectories for Lorentzian manifolds of splitting type.