  We consider strongly coupled competitive elliptic systems that arise in the
study of two-component Bose-Einstein condensates. As the coupling parameter
tends to infinity, solutions that remain uniformly bounded are known to
converge to a segregated limiting profile, with the difference of its
components satisfying a limit scalar PDE. In the case of radial symmetry, under
natural non-degeneracy assumptions on a solution of the limit problem, we
establish by a perturbation argument its persistence as a solution to the
elliptic system.
