Gravitational stability of dark energy in galaxies and clusters of
  galaxies
  We analyze the behavior of the scalar field as dark energy of the Universe in
a static world of galaxies and clusters of galaxies. We find the analytical
solutions of evolution equations of the density and velocity perturbations of
dark matter and dark energy, which interact only gravitationally, along with
the perturbations of metric in a static world with background Minkowski metric.
Using them it was shown that quintessential and phantom dark energy in the
static world of galaxies and clusters of galaxies is gravitationally stable and
can only oscillate by the influence of self-gravity. In the gravitational field
of dark matter perturbations it is able to condense monotonically, but the
amplitude of density and velocity perturbations on all scales remains small. It
was illustrated also, that the "accretion" of phantom dark energy in the region
of dark matter overdensities causes formation of dark energy underdensities -
the regions with negative amplitude of density perturbations of dark energy.
