Semiclassical states for a static supercritical Klein–Gordon–Maxwell–Proca system on a closed Riemannian manifold

Abstract

We establish the existence of semiclassical states for a nonlinear Klein–Gordon–Maxwell–Proca system in static form, with Proca mass [Formula: see text] on a closed Riemannian manifold. Our results include manifolds of arbitrary dimension and allow supercritical nonlinearities. In particular, we exhibit a large class of three-dimensional manifolds on which the system has semiclassical solutions for every exponent [Formula: see text] The solutions we obtain concentrate at closed submanifolds of positive dimension as the singular perturbation parameter goes to zero.