Existence of non-collision periodic solutions for second order singular dynamical systems

Abstract

In this paper, we study the existence of non-collision periodic solutions for the second order singular dynamical systems. We consider the systems where the potential has a repulsive or attractive type behavior near the singularity. The proof is based on Schauder's fixed point theorem involving a new type of cone. The so-called strong force condition is not needed and the nonlinearity could have sign changing behavior. We allow that the Green function is non-negative, so the critical case for the repulsive case is covered. Recent results in the literature are generalized and improved.