The present article deals with the positive solutions of a periodically perturbed Duffing type equation with singularity of the form u′′−u−α=e(t) and its damped counterpart u′′+cu′−u−α=e(t), for α≥1. Using a result on monotonicity for the period function of an associated planar autonomous system, we prove the existence of infinitely many subharmonic solutions, as well as the presence of chaotic dynamics, for some T-periodic forcing terms with negative mean value.
