Quasilinear asymptotically periodic Schrödinger equations with subcritical growth

Abstract 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 H 1 ( R N ) and satisfies the geometric hypotheses of the Mountain Pass Theorem.

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