SEQUENCES OF SMALL HOMOCLINIC SOLUTIONS FOR DIFFERENCE EQUATIONS ON INTEGERS

In this article, we determine a concrete interval of positive parameters lambda, for which we prove the existence of infinitely many homoclinic solutions for a discrete problem -Delta (a(k)phi(p) (Delta u(k - 1)) vertical bar b(k)phi(p) (u(k)) = lambda f (k, u(k)), k is an element of Z, where the nonlinear term f : Z x R -> R has an appropriate oscillatory behavior at zero. We use both the general variational principle of Ricceri and the direct method introduced by Faraci and Kristaly [11].