Existence of positive solution for nonlinear fourth-order difference equations

Let T be an integer with T >= 5 and let T(2) = {2, 3, ..., T}. We show the existence and multiplicity of positive solutions of the boundary value problem of nonlinear fourth-order difference equation Delta(4)u(t-2) - lambda f(t, u(t)) = 0, t is an element of T(2), u(1) = u(T + 1) = Delta(2)u(0) = Delta(2)u(T) = 0, where A is a parameter, f : T(2) x vertical bar 0, infinity) -> (0, infinity) is continuous. (C) 2010 Elsevier Ltd. All rights reserved.