Equações de Schrödinger quaselineares com potenciais singulares ou se anulando no infinito - Carvalho, Gilson Mamede de (2016)
In this work, we study existence of standing wave solution for a class of quasilinear Schrödinger equations involving potentials that may be singular at the origin or vanishing at infinity. For dimensions bigger than two, we consider nonlinearities with subcritical growth. In dimension two, we work with nonlinearities having exponential critical growth. To obtain our results, we have used variational techniques, more specifically, a version of the Mountain Pass Theorem, a regularity result of Brézis-Kato type, arguments of symmetrical criticality principle type, Moser iteration method and a Trudinger-Moser type inequality.