Layer Profiles of Solutions to Elliptic Problems under Parameter-Dependent Boundary Conditions

We consider the unique positive solution to the equation Δu = ur in Ω, where r > 1 and Ω is a smooth bounded domain of ℝN, under one of the boundary conditions u = λ , &#8706u/&#8706ν = λ, &#8706u/&#8706ν = λu or &#8706u/&#8706ν = λu – uq on &#8706Ω, q > 1. The main interest is determining the exact layer behavior of this solution near &#8706Ω 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.