The Robin problem for quasilinear equations with critical growth of the right-hand side

We consider the Robin problem for an equation driven by $p$-Laplacian with a critical right-hand side. For the semilinear case ($p=2$), this problem was investigated by X.-J. Wang (1991). We use a variant of the concentration-compactness method by P.-L. Lions and give some sharp sufficient conditions for the existence of the least energy solution.