Existência de soluções para equações de Schrödinger quasilineares com potencial se anulando no infinito.

Abstract

In this work we study questions related to the existence of positive solutions for some classes of quasilinear Schrödinger equations, with hypotheses on the potential that permit this potential to vanish at infinity. In order to use variational methods to obtain our results, we make some changes of variables to obtain some semilinear equations, whose associated functionals are well defined in a classical Sobolev spaces. We also work with these equations on an Orlicz “type” space whose energy functional satisfy the geometric properties of the Mountain Pass Theorem. We still use the penalty technique due to Del Pino and Felmer and the Moser iteration method to obtain estimates in L∞ norm, which are fundamental to our study.