Existence results for some elliptic equations involving the fractional Laplacian operator and critical growth

• Autor(a) principal: Araújo, Yane Lísley Ramos
• Data de Publicação: 2015
• 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/9252
• topic: Laplaciano fracionário; Métodos variacionais; Desigualdade de Trudinger- Moser; Expoente crítico de Sobolev; Fractional Laplacian; Variational methods; Trudinger-Moser's inequality; Critical Sobolev exponent; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we prove some results of existence and multiplicity of solutions for equations of the type ( ) u + V (x)u = f(x; u) in RN; where 0 < < 1, N 2 , ( ) denotes the fractional Laplacian, V : RN ! R is a continuous function that satisfy suitable conditions and f : RN R ! R is a continuous function that may have critical growth in the sense of the Trudinger-Moser inequality or in the sense of the critical Sobolev exponent. In order to obtain our results we use variational methods combined with a version of the Concentration-Compactness Principle due to Lions.