Positive solutions of a singular boundary value problem for systems of second-order differential equations

In this paper, we establish the conditions for the existence of positive solutions of a singular boundary value problem with two second-order differential equations. The development is based on a new maximum principle for the operator L2u=u″-2au″+(a2+b2)u under periodic boundary conditions and a fixed-point theorem in cones. When the eigenvalue λ lies in certain range, the boundary value problem in question has at least one positive solution. Our results include, extend and improve some previous results.