Infinitely many homoclinic solutions for second order difference equations with p-laplacian

By using critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation < a(k)p(<u(k 1)) < + b(k)p(u(k)) = f(k, u(k))), k Z, where p > 1 is a real number, p(t) = |t|p2t for t R, > 0 is a parameter, a, b : Z (0,), and f : Z × R R is a continuous function in the second variable. Some known work in the literature is extended.