On a class of singular Sturm–Liouville periodic boundary value problems

Keeping in mind the singular model for the periodic oscillations of the axis of a satellite in the plane of the elliptic orbit around its center of mass, we give sufficient conditions for the solvability of a class of singular Sturm–Liouville equations with periodic boundary value conditions. To this end, under a suitable change of variables, we present a new existence result for problems defined in the real half-line.