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

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 Poincaré–Birkhoff theorem, while for the second one, we consider a two-point boundary conditions of Neumann type.