The paper discusses the existence of positive solutions, dead-core solutions, and pseudo-dead-core solutions of the singular problem φ u λf t, u, u , u 0 −αu 0 A, u T βu 0 γu T A. Here λ is a positive parameter, α > 0, A > 0, β ≥ 0, γ ≥ 0, f is singular at u 0, and f may be singular at u 0.