  The Sturm-Liouville eigenvalue equation for eigenmodes of the radial
oscillations is determined for spherically symmetric perfect fluid
configurations in spacetimes with a nonzero cosmological constant and applied
in the cases of configurations with uniform distribution of energy density and
polytropic spheres. It is shown that a repulsive cosmological constant rises
the critical adiabatic index and decreases the critical radius under which the
dynamical instability occurs.
