The lusternik-schnirelman method relates the topology of manifolds with the critical points of functionals defined on them, giving lower bounds for the number of critical points in terms of the lusternik-schnirelmann category.

Is there some reference for the lusternik-schnirelman method (ensuring existence of at least cat(x) critical points for a functional defined on a banach manifold (x), in the context of quantitative deformation, as understood by Willem?).

The functional is not asumed to satisfy palais-smale condition (guaranteed by a deformation property with respect to compact critical sets), but rather a quantitative deformation lemma with respect to possibly noncompact critical sets.