Interaction between the geometry of the boundary and positive solutions of a semilinear neumann problem with critical nonlinearity

We consider the problem: -Δu + λu = un + 2)(n - 2, u > 0 in Ω , ∂u/∂v = 0 on ∂Ω, where Ω is a bounded smooth domain in Rn (n ≥ 3). We show that, for λ large, least-energy solutions of the above problem have a unique maximum point Pλ on ∂Ω and the limit points of Pλ, as λ → ∞ are contained in the set of the points of maximum mean curvature. We also prove that, if ∂Ω has k peaks then the equation has at least k solutions for λ large