Quasilinear asymptotically periodic Schr?dinger equations with critical growth

摘要

It is established the existence of solutions for a class of asymptotically periodic quasilinear elliptic equations in ?~N with critical growth. Applying a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in H~1({?}~N) and satisfy the geometric hypotheses of the Mountain Pass Theorem. The Concentration-Compactness Principle and a comparison argument allow to verify that the problem possesses a nontrivial solution.