  We study linear and nonlinear stability of asymptotically AdS$_4$ solutions
in Einstein-Maxwell-scalar theory. After summarizing the set of static
solutions we first examine thermodynamical stability in the grand canonical
ensemble and the phase transitions that occur among them. In the second part of
the paper we focus on nonlinear stability in the microcanonical ensemble by
evolving radial perturbations numerically. We find hints of an instability
corner for vanishingly small perturbations of the same kind as the ones present
in the uncharged case. Collapses are avoided, instead, if the charge and mass
of the perturbations come to close the line of solitons. Finally we examine the
soliton solutions. The linear spectrum of normal modes is not resonant and
instability turns on at extrema of the mass curve. Linear stability extends to
nonlinear stability up to some threshold for the amplitude of the perturbation.
Beyond that, the soliton is destroyed and collapses to a hairy black hole. The
relative width of this stability band scales down with the charge Q, and does
not survive the blow up limit to a planar geometry.
