Periodic orbits for radially symmetric systems with singularities and semilinear growth (Q681255)

The authors study a radially symmetric singular system of the type \[ \ddot x+f(t,| x|)\frac{x}{| x|}=0 \] with \(f\) being \(T\)-periodic in \(t\). They assume some kind of repulsive condition at \(0\), while at \(+\infty\) there is a nonresonance condition related to the eigenvalues of the asymptotic bounding linear problems. As a conclusion, they obtain the existence of periodic solutions with minimal period \(kT\), for every sufficiently large integer number \(k\).