A remark on periodic solutions of singular Hamiltonian systems

Abstract.

In this note we study the existence of non-collision periodic solutions for singular Hamiltonian systems with weak force. In particular for potential $V(t,q) \sim - \frac{1}{{{\text{dist}}(q,D)^{\alpha} }},$ where D is a compact C³-surface in $\mathbb{R}^{N} ,$ we prove the existence of a non-collision periodic solution.