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

Abstract

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 L 2 u = u ″ - 2 au ″ + ( a 2 + b 2 ) 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.