A multiplicity result for Hamiltonian systems with mixed periodic-type and Neumann-type boundary conditions

Abstract: We investigate the multiplicity of solutions for a Hamiltonian system coupling two systems associated with mixed boundary conditions. Corresponding to the first system, we impose periodic boundary conditions and assume the twist assumption commonly used for the Poincar\'e--Birkhoff theorem, while for the second one, we consider a two-point boundary conditions of Neumann type.