Boundary layers to a singularly perturbed Klein-Gordon-Maxwell-Proca system on a compact Riemannian manifold with boundary

We study the semiclassical limit to a singularly perturbed nonlinear Klein-Gordon-Maxwell-Proca system, with Neumann boundary conditions, on a Riemannian manifold M with boundary. We exhibit examples of manifolds, of arbitrary dimension, on which these systems have a solution which concentrates at a closed submanifold of the boundary of M , forming a positive layer, as the singular perturbation parameter goes to zero. Our results allow supercritical nonlinearities and apply, in particular, to bounded domains in R^n . Similar results are obtained for the more classical electrostatic Klein-Gordon-Maxwell system with appropriate boundary conditions.