Layer profiles of solutions to elliptic problems under parameter-dependent boundary conditions

摘要

We consider the unique positive solution to the equation Δu = u ~r in,where r > 1 and Ω is a smooth bounded domain of ?~N, under one of the boundary conditions u = λ, ?u/?ν = λ, ?u/?ν = λu or ?u/?ν = λu - uq on ?, Ωq > 1. The main interest is determining the exact layer behavior of this solution near ? 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.