Multiple subharmonic solutions in Hamiltonian system with symmetries

In this paper, we prove the existence of infinitely many non-constant geometrically distinct symmetric subharmonic solutions and symmetric subharmonic brake orbits for symmetric Hamiltonian systems which are superquadratic at zero and infinity by combining iteration theory of Maslov-type indices under various boundary conditions, the Galerkin approximation arguments and link theorem of critical point theory. Fur-thermore, we prove the existence of multiple geometrically distinct symmetric subharmonic solutions and symmetric subharmonic brake orbits for the symmetric Hamiltonian systems.(c) 2022 Elsevier Inc. All rights reserved.