Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities

Abstract

We prove the existence of multiple periodic solutions for weakly coupled parametrized systems with a singularity of repulsive type at the origin and linear growth at infinity. The proof is based on a higher dimensional Poincaré-Birkhoff theorem and the phase-plane analysis of the solutions.

Keywords

• periodic solutions
• weakly coupled systems
• systems with singularities
• poincaré-birkhoff theorem