Concentration-compactness principle and applications to nonlocal elliptic problems

• Ano de defesa: 2016
• Autor(a) principal: Souza, Diego Ferraz de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Concentração de compacidade; Laplaciano fracionário; Expoente crítico de Sobolev; Métodos variacionais; Concentration-compactness; Factional Laplacian; Critical Sobolev exponent; Variational methods; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9308

The main goal of this work is to analyze concentration-compactness principles for fractional Sobolev spaces based on the concentration compactness principle of P.-L. Lions and in the pro le decomposition for weak convergence in Hilbert spaces due to K. Tintarev and K.-H Fieseler. As application, we address questions on compactness of the associated energy functional to the following nonlocal elliptic problems, $' ''''''&' ''''''% p qsu fpx; uq in RN; p qsu apxqu fpx; uq in RN; $&% p qsu V pxqu Kpxq u fpx; uq gpx; uq in R3; p q Kpxqu2 in R3; where 0   s   1; 0     1; 2 4s ¥ 3; ¡ 0 and Kpxq ¥ 0 belongs to a suitable Lebesgue space. We obtain existence results for a wide class of possible singular potentials apxq; not necessarily bounded away from zero and for oscillatory nonlinearities in both subcritical and critical growth range that may not satisfy the Ambrosetti-Rabinowitz condition.