We consider the forced problem −Δ_pu − V(x)∣u∣^p−2u = f(x), where Δ_p is the p-Laplacian (1 < p < ∞) in a domain Ω ⊂ ℝ^N, V ≥ 0 and Q_V(u)≔ ∫_Ω ∣∇u∣^pdx − ∫_ΩV∣u∣^pdx satisfies the condition (A) below. We show that this problem has a solution for all f in a suitable space of distributions. Then we apply this result to some classes of functions V which in particular include the Hardy potential (1.5) and the potential V(x)= λ_1,p(Ω), where λ_1,p(Ω) is the Poincaré constant on an infinite strip.