Existence of Positive Solutions of a Discrete Elastic Beam Equation

Let T be an integer with T >= 5 and let T-2 = {2, 3,..., T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations del(4)u (t - 2) - ra(t)f(u(t)) = 0, t is an element of T-2, u(1) = u(T + 1) = Delta(2)u(0) = 0 = Delta(2)u(T) = 0, where r is a constant, a : T-2 -> (0,infinity), and f : [0,infinity) -> [0,infinity) is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.