Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions

We study the existence of positive solutions of the following fourth- order boundary value problem with integral boundary conditions, u((4)) (t) = f(t,u(t), u"(t)), t is an element of (0, 1), u(0) = integral(1)(0)g(s)u(s)ds, u (1) = 0, u"(0) = integral(1)(0)h(s)u" (s)ds, u"(1) = 0, where f : [0, 1] x [0,infinity) x (-infinity, 0] -> [0,+ 8) is continuous, g, h is an element of L(1)(0, 1] are nonnegative. The proof of our main result is based upon the Krein- Rutman theorem and the global bifurcation techniques.