Existence of periodic solutions for a 2nth-order nonlinear difference equation

The authors consider the 2nth-order difference equation Delta(n)(r(t-n)Delta n(t-n)(x)) + f(t, x(t)) = 0, n is an element of Z(3), t is an element of Z, where f : Z x R -> R is a continuous function in the second variable, f (t + T, z) = f (t, z) for all (t, Z) is an element of Z x R, r(t+T), = r(t) for all t is an element of Z, and T a given positive integer. By the Linking Theorem, some new criteria are obtained for the existence and multiplicity of periodic solutions of the above equation. (c) 2006 Elsevier Inc. All rights reserved.