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∈(0,1), u(0)=∫01g(s)u(s)ds, u(1)=0, u′′(0)=∫01h(s)u′′(s)ds, u′′(1)=0, where f:[0,1]×[0,+∞)×(-∞,0]→[0,+∞) is continuous, g,h∈L1[0,1] are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques.