Existence of positive solutions of a nonlinear fourth-order boundary value problem

In this paper, we study the existence of positive solutions of fourth-order boundary value problem u(4)(t)=f(t,u(t),u″(t)),t∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0,u(0)=u(1)=u″(0)=u″(1)=0, where f:[0,1]×[0,∞)×(−∞,0]→[0,∞)f:[0,1]×[0,∞)×(−∞,0]→[0,∞) is continuous. The proof of our main result is based upon the Krein–Rutman theorem and the global bifurcation techniques.