Existence of homoclinic solutions for p(n)p(n)-Laplacian Hamiltonian systems on Orlicz sequence spaces

By using the critical point theory, we establish some existence criteria to guarantee the second-order discrete p(n)p(n)-Laplacian systems Δ(|Δu(n−1)|p(n)−2u(n))−a(n)|u(n)|p(n)−2u(n)+∇W(n,u(n))=0Δ(|Δu(n−1)|p(n)−2u(n))−a(n)|u(n)|p(n)−2u(n)+∇W(n,u(n))=0 have at least one or infinitely many homoclinic orbits, where n∈Z,u∈RN, p:Z→R+p:Z→R+ and p(n)>1p(n)>1, a:Z→Ra:Z→R and W:Z×RN→RW:Z×RN→R are not periodic in nn.