Existence theorems for second-order discrete boundary value problems

This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type Delta[p(n) (Delta x(n-1))(delta)] + q(n)x(n)(delta) = f (n, x(n)), where delta > 0 is the ratio of odd positive integers, {p(n)} and {q(n)} are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions. (C) 2005 Elsevier Inc. All rights reserved.