  We study the stability against infinitesimal radial oscillations of neutron
stars generated by a set of equations of state obtained from first-principle
calculations in cold and dense QCD and constrained by observational data. We
consider mild and large violations of the conformal bound, $c_{s} =
1/\sqrt{3}$, in stars that can possibly contain a quark matter core. Some
neutron star families in the mass-radius diagram become dynamically unstable
due to large oscillation amplitudes near the core.
