Minimax Method for a Class of Hamiltonian Systems with Singular Potentials

摘要

This paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of Hamiltonian systems when a singular potential is present. The singularity satisfies the strong force condition of Gordon. When milder singularities are permitted, a notion of generalized T-periodic solution is introduced and we get existence and multiplicity results for such solutions.