Positive solutions for a class of singular semipositone boundary value problems

The paper presents sufficient conditions for the existence of positive solutions to the singular boundary value problem x″ = μq(t)f(t, x, x′), αx(0) − βx′(0) = a > 0, x(T) = 0 with q > 0 on (0, T), f ≥ 0 on a suitable subset of which may be singular at x = 0 and where either α, β ϵ (0, ∞) or α = 0, β = 1. Proofs are based on regularity and sequential techniques.