We consider the problem (Formula presented), where a > 0, c ≥ 0, α ∈ (0, 1), h:(0, 1] → (0, ∞) is a continuous function which may be singular at t = 0, but belongs to L1(0, 1) ∩ C1(0, 1), and g:[0, ∞) → [0, ∞) is a continuous function. We discuss existence, uniqueness, and non existence results for positive solutions for certain values of a, b and c. © 2018 Texas State University.