  The RPA monopole strength as well as the unperturbed particle-hole excitation
strength is studied, in which the strength in the continuum is properly treated
without discretizing unbound particle spectra. The model is the sef-consistent
Hartree-Fock calculation and the RPA Green's function method with Skyrme
interactions. Numerical examples are the Ni-isotopes, especially
$^{68}_{28}$Ni$_{40}$, in which an experimental observation of low-lying
socalled "pigmy resonance" with an appreciable amount of monopole strength at
12.9 $\pm$ 1.0 MeV was recently reported. In the present study it is concluded
that sharp monopole peaks with the width of the order of 1 MeV can hardly be
expected for $^{68}$Ni in that energy region. Instead, a broad shoulder of
monopole strength consisting of neutron excitations to non-resonant
one-particle states (called "threshold strength") with relatively low
angular-momenta $(\ell, j)$ is obtained in the continuum energy region above
the particle threshold, which is considerably lower than that of isoscalar
giant monopole resonance. In the case of monopole excitations of $^{68}$Ni
there are no unperturbed particle-hole states below 20 MeV, in which the
particle expresses a neutron (or proton) resonant state. It is emphasized that
in the theoretical estimate a proper treatment of the continuum is extremely
important.
