Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem

We study the existence of positive solutions of the nonlinear 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, which is not necessarily linearizable. Our approaches are based on Krein–Rutman theorem, topological degree theory and global bifurcation techniques.