Positive solutions of nonresonance semipositone singular Dirichlet boundary value problems

In the case where the nonlinearity term is allowed to change sign, we study the nonresonance semipositone singular Dirichlet boundary value problem (BVP) {−x″+ρp(t)x=λ[f(t,x)+g(t,x)],00 is a parameter, ρ>0 is a constant. We derive an interval of λ such that for any λ lying in this interval, the semipositone BVP has at least one positive solution if f is superlinear or sublinear. The results obtained improve and extend many recent results. Our approach is based on Krasnaselskii's fixed point theorem in cones.