Arbitrarily many solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity

We consider the sub- or supercritical Neumann elliptic problem -Δu + μu = u^N+2/N-2+ε, u > 0 in Ω; ∂u/∂n = 0 on ∂Ω, Ω being a smooth bounded domain in ℝ^N, N ≥ 4, μ > 0 and ε ≠ 0. Let H(x) denote the mean curvature at x. We show that for slightly sub- or supercritical problem, if ε min _x∈∂Ω H(x) > 0 then there always exist arbitrarily many solutions which blow up at the least curved part of the boundary as ε goes to zero.