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

TL;DR

This paper establishes multiple solutions for a Hamiltonian system with mixed boundary conditions, combining periodic and Neumann types, under specific twist and boundary assumptions.

Contribution

It introduces a novel approach to analyze Hamiltonian systems with mixed boundary conditions, extending multiplicity results to this new setting.

Findings

Proves existence of multiple solutions under combined boundary conditions.

Extends classical results like Poincaré--Birkhoff theorem to mixed boundary scenarios.

Provides new techniques for handling coupled boundary conditions in Hamiltonian systems.

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.