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

For a class of second-order discrete Hamiltonian systems ${\mathrm{\Delta }}^{2}x(t-1)-L(t)x(t)+V_x^{\mathrm{\prime }}(t,x(t))=0$, 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.