Soluções nodais para problemas elípticos semilineares com crescimento crítico exponencial

• Autor(a) principal: Pereira, Denilson da Silva
• 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/7449
• topic: Equação de Schrödinger; Crescimento crítico exponencial; Soluções nodais; Métodos variacionais; Desigualdade de Trudinger-Moser; Schrödinger equation; Exponential critical growth; Nodal solutions; Variational; Methods; Trudinger-Moser inequality; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we study existence, non-existence and multiplicity results of nodal solutions for the nonlinear Schrödinger equation (P) -u + V (x)u = f(u) in ; where is a smooth domain in R2 which is not necessarily bounded, f is a continuous function which has exponential critical growth and V is a continuous and nonnegative potential. In the first part, we prove the existence of least energy nodal solution in both cases, bounded and unbounded domain. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole R2. In the second part, we establish multiplicity of multi-bump type nodal solutions. Finally, for V - 0, we prove a result of infinitely many nodal solutions on a ball. The main tools used are Variational methods, Lions's Lemma, Penalization methods and a process of anti-symmetric continuation.