2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223170Let W be a weight-homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this result to a particular family of planar polynomial systems having a nilpotent center without meromorphic first integral.13 pages, no figuresDynamical Systems34C07, 34C05, 34C14text