Existence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders.

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorAssunção, Ronaldo Brasileiro-
Autor(es): dc.creatorMiyagaki, Olimpio Hiroshi-
Autor(es): dc.creatorRodrigues, Bruno Mendes-
Data de aceite: dc.date.accessioned2025-08-21T15:44:18Z-
Data de disponibilização: dc.date.available2025-08-21T15:44:18Z-
Data de envio: dc.date.issued2019-06-11-
Data de envio: dc.date.issued2019-06-11-
Data de envio: dc.date.issued2017-
Fonte completa do material: dc.identifierhttp://www.repositorio.ufop.br/handle/123456789/11516-
Fonte completa do material: dc.identifierhttps://doi.org/10.1186/s13661-017-0783-z-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1022904-
Descrição: dc.descriptionWe consider the following elliptic problem: – div( |∇u| p–2∇u |y| ap ) = |u| q–2u |y| bq + f(x) in , u = 0 on ∂, in an unbounded cylindrical domain := (y,z) ∈ Rm+1 × RN–m–1;0< A < |y| < B < ∞ , where 1 ≤ m < N – p, q = q(a, b) := Np N–p(a+1–b) , p > 1 and A, B ∈ R+. Let p∗ N,m := p(N–m) N–m–p . We show that p∗ N,m is the true critical exponent for this problem. The starting point for a variational approach to this problem is the known Maz’ja’s inequality (Sobolev Spaces, 1980) which guarantees, for the q previously defined, that the energy functional associated with this problem is well defined. This inequality generalizes the inequalities of Sobolev (p = 2, a = 0 and b = 0) and Hardy (p = 2, a = 0 and b = 1). Under certain conditions on the parameters a and b, using the principle of symmetric criticality and variational methods, we prove that the problem has at least one solution in the case f ≡ 0 and at least two solutions in the case f ≡ 0, if p < q < p∗ N,m.-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Direitos: dc.rightsaberto-
Direitos: dc.rightsO periódico Boundary Value Problems permite o arquivamento da versão/PDF do editor no Repositório Institucional. Fonte: Sherpa/Romeo <http://www.sherpa.ac.uk/romeo/search.php?issn=1687-2762>. Acesso em: 20 out 2016.-
Palavras-chave: dc.subjectPositive solution-
Palavras-chave: dc.subjectDegenerated operator-
Palavras-chave: dc.subjectVariational methods-
Título: dc.titleExistence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders.-
Aparece nas coleções:Repositório Institucional - UFOP

Não existem arquivos associados a este item.