Problemas elípticos semilineares com potenciais que se anulam no infinito

• Ano de defesa: 2020
• Autor(a) principal: Rafaella Ferreira dos Santos Siqueira
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais
• Palavras-chave em Português: Matemática – Teses; Teorema do passo da montanha – Teses; Potenciais de Hardy – Teses
• Link de acesso: https://hdl.handle.net/1843/45610

this dissertation, we study a result of existence of positive solution u ∈ D1,2 (R N ) for the following class of elliptic equations −∆u + V (x)u = f(u) (x ∈ R N ) where the nonlinearity f : R → R is a continuous function having a subcritical or critical growth in the sense of Sobolev embeddings and the potential V : R N → R is a continuous, non-negative function which can vanish at infinity, that is, V (x) → 0 as |x| → ∞. We also study a result of existence of positive ground state solution u ∈ D1,2 (R N ) for the following class of elliptic equations −∆u + V (x)u = K(x)f(u)(x ∈ R N ) where N > 3, the nonlinearity f : R → R is a continuous function having a quasi critical growth, and V , K : R N → R are continuous, non-negative functions, the potential V can vanish at infinity and K verifies growth conditions dependent on V . Key-words Potential vanishing at infinity, penalization method, Moser iteration scheme, mountain pass theorem, Hardy-type inequality.