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 [pn( xn−1)δ] + qnxδn = f (n,xn), where δ > 0 is the ratio of odd positive integers, {pn} and {qn} 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. © 2005 Elsevier Inc. All rights reserved