We investigate the problem of generation of MHD ballooning eigenperturbations in the inner magnetosphere of the Earth in the dipole geometry of the geomagnetic field with consideration for the ionospheric boundary conditions. The ionosphere is supposed to be a thin layer with finite conductivity. We put the particular attention to the study of the influence of ionospheric conductivity on the stability of the above-mentioned perturbations. It is demonstrated that in the case of insulating ionosphere flute perturbations are generated. An analytical instability criterion for the perturbations is derived. When the ionosphere is conductive, unstable MHD perturbations are provided mostly by ballooning modes. Their instability criterion is stricter than that of flute modes. In the case of resistive ionosphere, stable toroidal Alfven waves are slowly decaying.