Multiplicity of solutions for critical singular problems

• Autor(a) principal: Miyagaki, Olimpio Hiroshi
• Data de Publicação: 2006
• Outros Autores: Assuncao, Ronaldo B., Carrião, Paulo Cesar
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: https://doi.org/10.1016/j.aml.2005.10.004; http://www.locus.ufv.br/handle/123456789/22397
• topic: Degenerate quasilinear equation; p-Laplacian; Compactness– concentration; Variational methods

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.