Periodic Solutions And Ground State Solutions Of Several Types Of Second-order Hamiltonian Systems

In this paper,we mainly study the existence of periodic solutions and ground state solutions of second-order Hamilton systems.Firstly,we consider a periodic solution of second-order Hamilton systems:(?) we are concerned with the existence of a periodic solution for second order Hamiltonian systems under a new subquadratic growth condition by using the minimax methods in critical point theory,specially,a local linking theorem.Secondly,we consider a periodic solution and a ground state solution of second-order Hamilton systems:(?) we are concerned with the existence of a periodic solution for second order Hamiltonian systems by using mountain pass theorem.Based on the Nehari manifold,we also obtain a ground state solution.Finally,we consider a ground state sign-changing solution of second-order Hamilton systems:(?) we study the ground state sign-changing solution for second order Hamiltonian system by using the Nehari manifold.