EXISTENCE ANDA PRIORIBOUNDS FOR ELECTROSTATIC KLEIN–GORDON–MAXWELL SYSTEMS IN FULLY INHOMOGENEOUS SPACES

Abstract

We prove the existence and uniform bounds for the electrostatic Klein–Gordon–Maxwell systems in the inhomogeneous context of a compact Riemannian manifold when the mass potential, balanced by the phase, is small in a quantified sense. Phase compensation for the electrostatic Klein–Gordon–Maxwell systems and the positive mass theorem are used in a crucial way.