Periodic orbits of a singular superlinear planar system (Q314484)

The authors study the existence of periodic orbits for a system in \({\mathbb R}^2\)of the type \[ \ddot x+a(t)x=f(t,|x|)\frac{x}{|x|}. \] The singularity at the origin is of repulsive type, and the nonlinearity may have a superlinear growth at \(+\infty\). Concerning the continuous and periodic function \(a(t)\), it is necessary to assume that the associated Green function is positive. The main theorem is rather technical, but a nice corollary is illustrated at the end of the paper.