Positive periodic solutions for planar differential systems with repulsive singularities on the axes

In this paper we provide an existence result of periodic solutions to planar systems having a repulsive singularity on both the axes. We require a nonresonance assumption, related to the spectrum of the periodic problem associated to the Steenʹs planar system { − y ′ = − c x 3 + μ x , x ′ = − d y 3 + ν y , x > 0 , y > 0 , which is isochronous (see [15]). As a particular case we obtain the existence of periodic solutions to a periodically perturbed Steenʹs planar system.