Periodic Solutions for a Class of Non-coercive Hamiltonian Systems

Abstract

We prove the existence of non-constant T-periodic orbits of the Hamiltonian system q̇ = Hp(t, p(t), q(t)) ṗ = -Hq(t, p(t), q(t)). where H is a T-periodic function in t, non-convex and non-coercive in (p, q), and has the form H(t, p, q) ∽ |q|α (|p|β - 1) with α > β > 1.