2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223867We consider an Abelian Gauge Theory in R4 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. We assume that the nonlinear term is such that the energy functional is positive; this fact makes the theory more suitable for physical models. A three dimensional vortex is a finite energy, stationary solution of these equations such that the matter field has nontrivial angular momen- tum and the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of three dimensional vortex-solutions.Mathematical PhysicsAnalysis of PDEs47J30 (primary), 35J50, 81V10 (secondary)text