We consider a nonlinear equation with a monotone operator acting in W^{1,p}_0 (Ω), a lower order term u |u|^(n-1), and a source term in L^m (Ω) with a poor summability m > 1 or even m = 1. When the power n increases and tends to ∞, we prove that the (conveniently defined) solution of this problem converges (in a convenient sense) to the solution of the variational inequality posed on the convex set {v ∈ W^{1,p}_0 (Ω) : |v(x)| ≤ 1}. This paperi has been published in Boll. Un. Mat. Ital., 10, (2017), pp. 617-625, doi 10.1007/s40574-016-0093-x