  We complete the stability study of general relativistic spherically symmetric
polytropic perfect fluid spheres, concentrating attention to the newly
discovered polytropes containing region of trapped null geodesics. We compare
the methods of treating the dynamical stability based on the equation governing
infinitesimal radial pulsations of the polytropes and the related
Sturm-Liouville eigenvalue equation for the eigenmodes governing the
pulsations, to the methods of stability analysis based on the energetic
considerations. Both methods are applied to determine the stability of the
polytropes governed by the polytropic index n in the whole range 0 < n < 5, and
the relativistic parameter {\sigma} given by the ratio of the central pressure
and energy density, restricted by the causality limit. The critical values of
the adiabatic index for stability are determined, together with the critical
values of the relativistic parameter {\sigma}. For the dynamical approach we
implemented a numerical method which is independent on the choice of the trial
function, and compare its results with the standard trial function approach. We
found that the energetic and dynamic method give nearly the same critical
values of {\sigma}. We found that all the configurations having trapped null
geodesics are unstable according to both methods.
