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

Abstract

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 Steen's planar system{-y'=-cx3+μx,x'=-dy3+νy,x>0,y>0, which is isochronous (see [15]). As a particular case we obtain the existence of periodic solutions to a periodically perturbed Steen's planar system. © 2014 Elsevier Inc.