Semiclassical states for a static supercritical Klein-Gordon-Maxwell-Proca system on a closed Riemannian manifold (Q2800061)

The authors prove existence of semiclassical states for a nonlinear Klein-Gordon-Maxwell-Proca system in static form, with Proca mass 1, over a closed Riemannian manifold. The results include manifolds of arbitrary dimension and allow supercritical nonlinearities. In particular, a large class is exhibited of three-dimensional manifolds on which the system has semiclassical solutions for every exponent \(p>2\). The solutions obtained concentrate at closed submanifolds of positive dimension as the singular perturbation parameter goes to zero.