2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126527We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.Keywords: Duffing equation; Periodic solution; StabilityClassical Analysis and ODEs34C10; 34C25text