  The equations describing the adiabatic, small radial oscillations of general
relativistic stars are generalized to include the effects of a cosmological
constant. The generalized eigenvalue equation for the normal modes is used to
study the changes in the stability of the homogeneous sphere induced by the
presence of the cosmological constant. The variation of the critical adiabatic
index as a function of the central pressure is studied numerically for
different trial functions. The presence of a large cosmological constant
significantly increases the value of the critical adiabatic index. The
dynamical stability condition of the homogeneous star in the Schwarzschild-de
Sitter geometry is obtained and several bounds on the maximum allowable value
for a cosmological constant are derived from stability considerations.
