Multibump solutions of a class of second-order discrete Hamiltonian systems

For a class of second-order discrete Hamiltonian systems $\Delta^2x(t-1)-L(t)x(t)+V'_x(t,x(t))=0$, we investigate the existence of homoclinic orbits by applying variational method, where $L$ and $V(\cdot,x)$ are periodic functions. Further, we show that there exist either uncountable many homoclinic orbits or multibump solutions under certain conditions