Periodic, quasi-periodic and unbounded solutions of radially symmetric systems with repulsive singularities at resonance

Abstract

In this paper, we are concerned with periodic solutions, quasi-periodic solutions and unbounded solutions for radially symmetric systems with singularities at resonance, which are 2π-periodic in time. The method is based on the qualitative analysis of Poincare map with action-angle variables. The existence of infinitely many periodic and quasi-periodic solutions or unbounded motions depends on the oscillatory properties of a certain function.