  Using the density-dependent Hartree-Fock approximation and Skyrme forces
together with the scaling method and constrained Hartree-Fock calculations, we
obtain the average energies of the isoscalar giant monopole resonance. The
calculations are done along several isotopic chains from the proton to the
neutron drip lines. It is found that while approaching the neutron drip line,
the scaled and the constrained energies decrease and the resonance width
increases. Similar but smaller effects arise near the proton drip line,
although only for the lighter isotopic chains. A qualitatively good agreement
is found between our sum rule description and the presently existing random
phase approximation results. The ability of the semiclassical approximations of
the Thomas-Fermi type, which properly describe the average energy of the
isoscalar giant monopole resonance for stable nuclei, to predict average
properties for nuclei near the drip lines is also analyzed. We show that when
hbar corrections are included, the semiclassical estimates reproduce, on
average, the quantal excitation energies of the giant monopole resonance for
nuclei with extreme isospin values.
