Positivity and lower and upper solutions for fourth order boundary value problems

This paper is devoted to the study the boundary value problem {u(4)(t)=f(t,u(t))for all t∈I=[0,1],u(0)=u(1)=u″(0)=u″(1)=0. We prove the existence of at least one, two or three solutions in the presence of a pair of, not necessarily ordered, lower and upper solutions.The proof follows from maximum principles related to the operator u(4)+Muu(4)+Mu and Amann’s three solutions theorem.