Critical singular problems via concentration-compactness lemma

• Autor(a) principal: Miyagaki, Olimpio Hiroshi
• Data de Publicação: 2007
• Outros Autores: Assunção, 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.jmaa.2006.03.002; http://www.locus.ufv.br/handle/123456789/23220
• topic: Degenerate quasilinear equation; P-Laplacian; Variational methods; Compactness-concentration

In this work we consider existence and multiplicity results of nontrivial solutions for a class of quasilinear degenerate elliptic equations in RN of the form (P)−div[|x|−ap|∇u|p−2∇u]+λ|x|−(a+1)p|u|p−2u=|x|−bq|u|q−2u+f, where x∈RN, 1<p<N, q=q(a,b)≡Np/[N−p(a+1−b)], λ is a parameter, 0⩽a<(N−p)/p, a⩽b⩽a+1, and f∈(Lbq(RN))∗. We look for solutions of problem (P) in the Sobolev space Da1,p(RN) and we prove a version of a concentration-compactness lemma due to Lions. Combining this result with the Ekeland's variational principle and the mountain-pass theorem, we obtain existence and multiplicity results.