Multiplicity results for an anisotropic equation with subcritical or critical growth
In this work we show some multiplicity results for the anisotropic equation − XN i=1 ∂ ∂xi ∂u ∂xi pi−2 ∂u ∂xi = gλ(u) in Ω, and u = 0 on ∂Ω, where Ω ⊂ℝN is a bounded smooth domain, 1 < p1 ≤ p2 ≤ . . . ≤ pN and λ is a positive parameter. Using genus theory, we study the subcritical case gλ(u) = λ|...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47890 |
| Acceso en línea: | http://hdl.handle.net/11441/47890 https://doi.org/10.1515/ans-2015-0206 |
| Access Level: | acceso abierto |
| Palabra clave: | Anisotropic operator Genus theory Subcritical or critical growth |
| Sumario: | In this work we show some multiplicity results for the anisotropic equation − XN i=1 ∂ ∂xi ∂u ∂xi pi−2 ∂u ∂xi = gλ(u) in Ω, and u = 0 on ∂Ω, where Ω ⊂ℝN is a bounded smooth domain, 1 < p1 ≤ p2 ≤ . . . ≤ pN and λ is a positive parameter. Using genus theory, we study the subcritical case gλ(u) = λ|u|q−2u with q ∈ (1, pN) and the critical case gλ(u) = λ|u|q−2u +|u|p*−2u with q ∈ (1, p1) and p* = N| p̅/(N−p̅), with p̅ the harmonic mean of the pi’s. |
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