2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142583In this paper we consider an Abelian Gauge Theory in R^4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein-Gordon-Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. A three dimensional vortex is a finite energy solution of these equations in which the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of vortex-solutions.31 pagineAnalysis of PDEsMathematical Physics35J50; 81T13text