We consider the problem-Δpu = aup-1-bu γ -1-c/uα, x ∈Ω, u = 0, x ∈ ∂Ω, whereΔpu = div(|∇u|p-2∇u) , p > 1, Ω is a smooth bounded domain in ℝn, a > 0, b > 0, c ≥ 0, γ > p and α ∈ (0, 1). Given a, b, γ and α, we establish the existence of apositive solution for small values of c. These results are also extended to corresponding exterior domain problems. Also, a bifurcation result for the case c = 0 ispresented. © 2013 Goddard II et al.