2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78418We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that the higher-degree vortices (|n| > 1) are stable for k < 1 and unstable for k > 1. This resolves a long-standing conjecture.28 pages, LatexAnalysis of PDEsMathematical Physics35J60 (Primary), 82D55 (Secondary)text