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URI permanente para esta coleçãohttps://locus.ufv.br/handle/123456789/11799
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Item Critical singular problems via concentration-compactness lemma(Journal of Mathematical Analysis and Applications, 2007-02-01) Miyagaki, Olimpio Hiroshi; Assunção, Ronaldo B.; Carrião, Paulo CesarIn 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, 1Item Critical singular problems via concentration-compactness lemma(Journal of Mathematical Analysis and Applications, 2007-02-01) Miyagaki, Olimpio Hiroshi; Assunção, Ronaldo B.; Carrião, Paulo CesarIn 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, 1Item Multiplicity of solutions for critical singular problems(Applied Mathematics Letters, 2006-08) Miyagaki, Olimpio Hiroshi; Assuncao, Ronaldo B.; Carrião, Paulo CesarIn 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.