On Hamiltonian systems with critical Sobolev exponents

• Ano de defesa: 2022
• Autor(a) principal: Guimaraes, Angelo
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Critical dimension; Critical hyperbola; Dimensão crítica; Hipérbole crítica; Lane-Emden systems; Positive solutions; Sistemas de Lane-Emden; Solução positiva
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-07112022-153517/

In this thesis we consider lower order perturbations of the critical Lane-Emden system posed on a bounded smooth domain Ω ⊂ RN, with N ≥ 3, inspired by the classical results of Brezis and Nirenberg (BRÉZIS; NIRENBERG, 1983). We solve the problem of finding a positive solution for all dimensions N ≥ 4. For the critical dimension N = 3 we show a new phenomenon, not observed for scalar problems. Namely, there are parts on the critical hyperbola where solutions exist for all 1-homogeneous or subcritical superlinear perturbations and parts where there are no solutions for some of those perturbations.