Periodic solutions for a class of second-order Hamiltonian systems

Abstract

Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.

Keywords

• Second order Hamiltonian systems
• eigenvalue problem
• periodic solutions
• critical points
• multiple solutions.