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 , where 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.