On positive solutions for a class of singular quasilinear elliptic systems
We study through the lower and upper-solution method, the existence of positive weak solution to the quasilinear elliptic system with weights ⎧ ⎪ −div(|x|−ap |∇u|p−2 ∇u) = λ|x|−(a+1)p+c1 uα v γ in Ω, ⎨ −div(|x|−bq |∇v|q−2 ∇v) = λ|x|−(b+1)q+c2 uδ v β in Ω, ⎪ ⎩ u=v=0 on ∂Ω, −p −q where Ω is a bounded...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2007 |
| País: | Brasil |
| Recursos: | Universidade Federal de Viçosa (UFV) |
| Repositório: | LOCUS Repositório Institucional da UFV |
| Idioma: | inglês |
| OAI Identifier: | oai:locus.ufv.br:123456789/22425 |
| Acesso em linha: | https://doi.org/10.1016/j.jmaa.2007.01.018 http://www.locus.ufv.br/handle/123456789/22425 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Degenerate equations Comparison theorems Strong maximum principle Positive solutions Quasilinear equations |
| Resumo: | We study through the lower and upper-solution method, the existence of positive weak solution to the quasilinear elliptic system with weights ⎧ ⎪ −div(|x|−ap |∇u|p−2 ∇u) = λ|x|−(a+1)p+c1 uα v γ in Ω, ⎨ −div(|x|−bq |∇v|q−2 ∇v) = λ|x|−(b+1)q+c2 uδ v β in Ω, ⎪ ⎩ u=v=0 on ∂Ω, −p −q where Ω is a bounded smooth domain of RN , with 0 ∈ Ω, 1 < p, q < N , 0 a < N p , 0 b < N q , 0 α < p − 1, 0 β < q − 1, δ, γ , c1 , c2 > 0 and θ := (p − 1 − α)(q − 1 − β) − γ δ > 0, for each λ > 0. |
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