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

• Autor(a) principal: Aires, José Fernando Leite
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/7450
• topic: Equações de Schrödinger quasilineares; Crescimento quasicrítico; Potenciais se anulando; Quasilinear Schrödinger equation; Quasicritical growth; Vanishing potentials; CIENCIAS EXATAS E DA TERRA::MATEMATICA

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 L1 norm, which are fundamental to our study.