Métodos variacionais, desigualdade do tipo Trudinger-Moser e aplicações

• Autor(a) principal: Santos, Izabela Andrade dos
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFS
• Texto Completo: https://ri.ufs.br/handle/riufs/5815
• topic: Matemática; Método variacional; Desigualdade de Trudinger-Moser; Soluções fracas; Equações diferenciais; Variational methods; Trudinger-Moser inequality; Weak solutions; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we are interested in establishing some variational methods, together with applications, that determine the existence and non uniqueness of weak solutions for the nonlinear elliptic partial differential equation −div (K(x)-u) = K(x)f(u) + h, x E R2, where K is an exponential weight, h is a linear functional and f is the nonlinearity that presents critical exponential growth. First of all, for the sake of convenience of the reader, this study shows detailed proofs of some classic results of the theory that involves these methods as, for example, the deformation and mountain pass theorems; and Ekeland’s variational principle. Second of all, we work with a Trudinger-Moser inequality that is related to a Sobolev space with weight K in order to achieve our aim.