2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59518We extend Lusternik-Schnirelmann theory to pairs $(f, ϕ)$, where $ϕ$ is a homotopy equivalence of a space $X$, $f$ is a function on $X$ which decreases along $ϕ$ and $(f, ϕ)$ satisfies a discrete analog of the Palais-Smale condition. The theory is carried out in an equivariant setting.23 pages, 1 figureDynamical SystemsClassical Analysis and ODEsGeometric Topologytext