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

For a class of second-order discrete Hamiltonian systems Δ2x(t-1)-L(t)x(t)+Vx′(t,x(t))=0, we investigate the existence of homoclinic orbits by applying variational method, where L   and V(·,x)V(·,x) are periodic functions. Further, we show that there exist either uncountable many homoclinic orbits or multibump solutions under certain conditions.