On eigenvalue intervals and eigenfunctions of fourth-order singular boundary value problems

Values of λ are determined for which there exist positive solutions of the fourth-order singular boundary value problems {x(4)(t)=λf(t,x(t)),t∈(0,1),x(0)=x(1)=0,x″(0)=x″(1)=0, where f∈C((0,1)×(0,∞),[0,∞)), λ>0 is parameter. For λ=1, we give criteria for the existence of eigenfunctions.