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Multiplicity results for an anisotropic equation with subcritical or critical growth

 

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Opened Access Multiplicity results for an anisotropic equation with subcritical or critical growth
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Author: Malcher Figueiredo, Giovany de Jesus
Rodrigues dos Santos Júnior, Joao
Suárez Fernández, Antonio
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2015-05
Published in: Advanced Nonlinear Studies, 15 (2), 377-394.
Document type: Article
Abstract: 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.
Cite: Malcher Figueiredo, G.d.J. y Rodrigues dos Santos Júnior, J. (2015). Multiplicity results for an anisotropic equation with subcritical or critical growth. Advanced Nonlinear Studies, 15 (2), 377-394.
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URI: http://hdl.handle.net/11441/47890

DOI: 10.1515/ans-2015-0206

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