A multiplicity result for periodic solutions of second order differential equations with a singularity

By the use of the Poincaré–Birkhoff fixed point theorem, we prove a multiplicity result for periodic solutions of a second order differential equation, where the nonlinearity exhibits a singularity of repulsive type at the origin and has linear growth at infinity. Our main theorem is related to previous results by Rebelo (1996, 1997) [4] and [5] and Rebelo and Zanolin (1996) [6] and [7], in connection with a problem raised by del Pino et al. (1992) [1].