Periodic Impact Motions at Resonance of a Particle Bouncing on Spheres and Cylinders

We investigate the existence of periodic trajectories of a particle, subject to a central force, which can hit a sphere or a cylinder. We will also provide a Landesman–Lazer-type condition in the case of a nonlinearity satisfying a resonance condition. Afterwards, we will show how such a result can be adapted to obtain a new result for the impact oscillator at resonance.