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

TL;DR

This paper proves the existence of semiclassical solutions for a supercritical Klein-Gordon-Maxwell-Proca system on closed Riemannian manifolds, including those with arbitrary dimensions and supercritical nonlinearities, with solutions concentrating on submanifolds.

Contribution

It establishes the existence of semiclassical states for the supercritical Klein-Gordon-Maxwell-Proca system on general closed manifolds, extending previous results to supercritical cases and higher dimensions.

Findings

Existence of semiclassical solutions on arbitrary-dimensional manifolds.

Solutions concentrate on positive-dimensional submanifolds.

Applicable for all exponents p>2 in 3D cases.

Abstract

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