  In this paper we study the existence of solution for a class of variational
inequality in whole $\mathbb{R}^N$ where the nonlinearity has a critical growth
for $N \geq 2$. By combining a penalization scheme found in del Pino and Felmer
[18] with a penalization method due to Bensoussan and Lions [9], we improve a
recent result by Alves, Barros and Torres [1].
