A class of first-order noncoercive discrete Hamiltonian systems are considered. Based on a generalized mountain pass theorem, some existence results of homoclinic orbits are obtained when the discrete Hamiltonian system is not periodical and need not satisfy the global Ambrosetti-Rabinowitz condition.
"Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems." J. Appl. Math. 2012 1 - 21, 2012. https://doi.org/10.1155/2012/720139