Quasilinear asymptotically periodic elliptic equations with critical growth

The existence of a nontrivial solution for a class of asymptotically periodic equations involving the pp-Laplacian operator in the euclidean space is established. The solutions are obtained by an application of the Mountain Pass Theorem and the Concentration-Compactness Principle. The lack of compactness due to the fact that the domain is unbounded is compensated by comparing the minimax level associated with the original problem and the minimax level associated with the periodic limit problem.