2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152349We consider a class of one--dimensional non--convex non--coercive problems in the Calculus of Variations. We prove an existence result for this class of problems using a Liapunov type theorem on the range of non--atomic measures.10 pages, plain TeX, no figuresFunctional AnalysisAn existence result for non-coercive non-convex problemstext