Quasilinear asymptotically periodic Schrödinger equations with subcritical growth

In this article the existence of one solution for a class of asymptotically periodic equations in the euclidean space is established. The basic tools employed here are the Mountain Pass Theorem and the Concentration–Compactness Principle. By using a change of variable, the quasilinear equation is reduced to a semilinear equation, whose respective associated functional is well defined in H1(RN)H1(RN) and satisfies the geometric hypotheses of the Mountain Pass Theorem.