2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157129We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential $ϕ=0$. This result, due to the lack of suitable embedding theorems for the vector potential $\A$ is achieved with the help of a penalization method.23 pages, no figuresAnalysis of PDEsMathematical Physics35J20; 35J60; 35Q60text