  We study the isospin asymmetry in the isoscalar (IS) excitations in the
mirror nuclei $^{14}$O and $^{14}$C by using the Hartree-Fock(HF)+random phase
approximation (RPA) linear response function theory with a Skyrme interaction
to take into account the continuum effect properly. The asymmetry in the IS
monopole, dipole responses is pointed out in the continuum near the particle
threshold with respect to the excitation energy and the sum rule strength. On
the other hand, no clear sign of the asymmetry is found in the giant resonance
(GR) region. In the quadrupole case, the calculated strengths of the mirror
nuclei show almost the same energy dependence from the threshold to the GR
region. It is found that the transition densities of the monopole response show
an extended halo structure near the threshold, while those of GR region show a
typical radial dependence of the compressional collective mode without any halo
effect. Contrary to the transition densities of the monopole response, those of
quadrupole response do not show any sign of the extended feature of wave
functions neither near the threshold nor the GR energy region. Calculated
strength distributions of the IS multipole states are compared with recent
experimental data obtained by the multipole decomposition analysis of $\alpha $
inelastic scattering on $^{14}$O.
