2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59486This paper is concerned with index pairs in the sense of Conley index theory for flows relative to pseudo-gradient vector fields for $C^1$-functions satisfying Palais-Smale condition. We prove a deformation theorem for such index pairs to obtain a Lusternik-Schnirelmann type result in Conley index theory.11 pages, a noncompact version of the previous resultsDynamical Systems37B30, 58E05text