Multiplicity of solutions for critical singular problems
In this work we deal with the class of critical singular quasilinear elliptic problems in R N of the form −div(|x|−ap |∇u| p−2 ∇u) = α|x|−bq |u|q−2 u + β|x|−dr k|u|r−2 u x ∈ RN , (P) where 1 < p < N, a < N/ p, a ≤ b < a + 1, α and β are positive parameters, q = q(a, b) ≡ N p/[N − p(a + 1...
| Autores: | , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2006 |
| País: | Brasil |
| Recursos: | Universidade Federal de Viçosa (UFV) |
| Repositório: | LOCUS Repositório Institucional da UFV |
| Idioma: | inglês |
| OAI Identifier: | oai:locus.ufv.br:123456789/22397 |
| Acesso em linha: | https://doi.org/10.1016/j.aml.2005.10.004 http://www.locus.ufv.br/handle/123456789/22397 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Degenerate quasilinear equation p-Laplacian Compactness– concentration Variational methods |
| Resumo: | In this work we deal with the class of critical singular quasilinear elliptic problems in R N of the form −div(|x|−ap |∇u| p−2 ∇u) = α|x|−bq |u|q−2 u + β|x|−dr k|u|r−2 u x ∈ RN , (P) where 1 < p < N, a < N/ p, a ≤ b < a + 1, α and β are positive parameters, q = q(a, b) ≡ N p/[N − p(a + 1 − b)] and d ∈ R. q/(q−r) Moreover, 1 < r < p∗ = N p/(N − p) and 0 ≤ k ∈ L r(d−b) (R N ). Multiplicity results are established by combining a version of the concentration–compactness lemma due to Lions with the Krasnoselski genus and the symmetric mountain-pass theorem due to Rabinowitz. |
|---|