Quasilinear asymptotically periodic Schrödinger equations with critical growth

摘要

It is established the existence of solutions for a class of asymptotically periodic quasilinear elliptic equations in with critical growth. Applying a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in 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.