Concentration on minimal submanifolds for a singularly perturbed Neumann problem

We consider the equation −ε2Δu+u=up in Ω⊆RN, where Ω is open, smooth and bounded, and we prove concentration of solutions along k-dimensional minimal submanifolds of ∂Ω, for N⩾3 and for k∈{1,…,N−2}. We impose Neumann boundary conditions, assuming 1