Infinitely many periodic solutions of planar Hamiltonian systems via the Poincaré–Birkhoff theorem

Abstract In this paper, we study the multiplicity of periodic solutions of one kind of planar Hamiltonian systems with a nonlinear term satisfying semilinear conditions. Using a generalized Poincaré–Birkhoff fixed point theorem, we prove that the system has infinitely many periodic solutions, provided that the time map tends to zero.