We study the positive periodic solutions of a periodically perturbed second-order nonlinear equation with a singularity, related to the so-called Liebau phenomenon, which has received great deal of interest in the past decade. Our main contribution concerns a global theorem about the monotonicity of the period map for the equation with constant coefficients. Then, as applications, we prove new bifurcation results for periodic solutions (harmonic and subharmonic), as well as the presence of complex dynamics for some periodic coefficients which are meaningful from a physical point of view.
