Periodic solutions of Hamiltonian systems coupling twist with generalized lower/upper solutions

The Hamiltonian systems considered in this paper are obtained by weakly coupling two systems hav-ing completely different behaviors. The first one satisfies the twist assumptions usually considered for the application of the Poincare-Birkhoff Theorem, while the second one presents the existence of some well -ordered lower and upper solutions. In the higher dimensional case, we also treat a coupling situation where the classical Hartman condition is assumed.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).