Ground state solutions and periodic solutions with minimal periods to second-order Hamiltonian systems

Abstract

In this paper, we study the existence of periodic solutions to second-order Hamiltonian systems. The nonlinear term has a special form, which satisfies a nondecreasing monotone assumption. Making use of a generalized Nehari manifold, we built the homomorphism between the Nehari manifold and the unit sphere of some space. Some sufficient conditions are obtained to guarantee the existence of periodic solutions with the prescribed minimal period to Hamiltonian systems. Our results extend the results in references.