Periodic second order superlinear Hamiltonian systems

Abstract

We study the existence of periodic solutions of a second order nonautonomous dynamical system including both the kinetic and potential terms. We assume little concerning the gradient of the potential other than continuity. This allows both sublinear and superlinear problems. We also study the existence of ground state solutions.

Some notes on a superlinear second order Hamiltonian system

“…In [35] the case when, among the others, ∇F (t, ξ) • ξ − µF (t, ξ) → +∞ as |ξ| → ∞ is considered. More recently, in [29,38], problem (1.1) has been studied when the right hand side is perturbed by a linear term B(t)u where B(t) is a symmetric matrix whose components are integrable functions.…”