Semiclassical states for a static supercritical   Klein-Gordon-Maxwell-Proca system on a closed Riemannian manifold
  We establish the existence of semiclassical states for a nonlinear Klein-Gordon-Maxwell-Proca system in static form, with Proca mass 1 on a closed Riemannian manifold.   Our results include manifolds of arbitrary dimension and allow supercritical nonlinearities. In particular, we exhibit a large class of 3-dimensional manifolds on which the system has semiclassical solutions for every exponent p>2. The solutions we obtain concentrate at closed submanifolds of positive dimension as the singular perturbation parameter goes to zero 
Monica Clapp and Marco Ghimenti and Anna Maria Micheletti
math.AP