Multidimensional boundary layers for a singularly perturbed Neumann problem

We prove concentration phenomena for the equation − \epsillon^2 \Delta u+u = u^p in a smooth bounded domain if R^n and with Neumann boundary conditions. The exponent p is greater than or equal to 1, and the parameter \epsilon is converging to zero. For a suitable sequence \epsilon_j \to 0, we prove the existence of positive solutions u_j concentrating at the whole boundary or at some of its components.