Homoclinic solutions for a second order difference equation with p-Laplacian

In this paper, we obtain new conditions under which the difference equation -Delta(a(k)phi(p)(Delta u(k - 1)) + b(k)phi(p)(u(k)) = lambda f (k, u(k)), k is an element of Z. has infinitely many homoclinic solutions, where p > 1 is a real number, phi(p)(t) = vertical bar t vertical bar(p) (2)t for t is an element of R, lambda > 0 is a parameter, a; b : Z -> (0, infinity), and f : Z x R -> R is continuous in the second variable. Some known results in the literature are extended and complemented. A variant of the fountain theorem is utilized in the proof of our theorem. (C) 2014 Elsevier Inc. All rights reserved.