Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem

we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problem Delta(4)u(t - 2) = lambda h(t)f(u(t)), t is an element of T-2, u(1) = u(T + 1) = Delta(2)u(0) = Delta(2)u(T) = 0, where lambda > 0, h : T-2 -> (0,infinity) is continuous, and f : R -> [0,infinity) is continuous, T > 4, T-2 = {2, 3, . . . , T}. The main tool is the Dancer's global bifurcation theorem.