  We consider an Einstein-scalar field model which is a consistent truncation
of ${\cal N}=8$ $D=4$ gauged supergravity, the scalar field possessing a
potential which is unbounded from below and a tachyonic mass above the
Breitenlohner-Freedman bound. We investigate the spherically symmetric
asymptotically anti-de Sitter soliton and black hole solutions, with the aim of
clarifying the asymptotics and the possible boundary conditions at infinity.
The emerging picture is contrasted with that found for an Einstein-scalar field
model with the same scalar mass and a quartic self-interaction term. We also
provide arguments for the existence of solitonic solutions which can be viewed
as non-linear continuation of the (probe) scalar multipolar clouds, with
emphasis on the dipole case. Apart from numerical results, exact solutions are
found for solitons with a monopole and dipole scalar field, as perturbations
around the AdS background.
