Radially symmetric systems with a singularity and asymptotically linear growth

We prove the existence of infinitely many periodic solutions for radially symmetric systems with a singularity of repulsive type. The nonlinearity is assumed to have a linear growth at infinity, being controlled by two constants which have a precise interpretation in terms of the Dancer-Fučik spectrum. Our result generalizes an existence theorem by Del Pino et al. (1992) [4], obtained in the case of a scalar second order differential equation.