We consider the boundary value problem (Pλ) −∆pu = λc(x)|u| p−2u + µ(x)|∇u| p + h(x) , u ∈ W1,p 0 (Ω) ∩ L∞(Ω) , where Ω ⊂ RN , N ≥ 2, is a bounded domain with smooth boundary. We assume c, h ∈ Lq (Ω) for some q > max{N/p, 1} with c 0 and µ ∈ L∞(Ω). We prove existence and uniqueness results in the coercive case λ ≤ 0 and existence and multiplicity results in the non-coercive case λ > 0. Also, considering stronger assumptions on the coefficients, we clarify the structure of the set of solutions in the non-coercive case.