  Conditions for intra and inter layer Coulomb interactions in multi-walled
carbon nanotubes are derived from stability of capacitance excitations. It is
pointed out, supposing the stability conditions are not satisfied, that the
system has unstable modes which correspond to a charge transfer between layers
or charge density oscillation in each layer depending on zero mode or non-zero
modes. It is argued that the stability conditions can be broken when the vacuum
polarization processes due to the massive bands are taken into account.
