Abstract
We consider the unique positive solution to the equation Δ\_u\_ = ur in Ω, where r > 1 and Ω is a smooth bounded domain of ℝ\_N\_, under one of the boundary conditions u = λ, ∂u/∂ν = λ, ∂u/∂ν = λ\_u\_ or ∂u/∂ν = λ\_u\_ – uq on ∂Ω, q > 1. The main interest is determining the exact layer behavior of this solution near ∂Ω in terms of the parameter λ as λ → ∞. Our analysis is completed with the study of the same type of problems involving the p-Laplacian operator.
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