Subharmonic solutions and homoclinic orbits of second order discrete Hamiltonian systems with potential changing sign

In this paper, a class of second order discrete Hamiltonian systems with periodicity assumptions is considered. Based on the critical point theory, some sufficient conditions for the existence of subharmonic solutions and homoclinic orbits are obtained. The results obtained extend the results in 2007 by relaxing the assumptions on the sign of the potential.