  Recently, static and spherically symmetric configurations of globally regular
self-gravitating scalar solitons were found. These configurations are unstable
with respect to radial linear perturbations. In this paper we study the
dynamical evolution of such configurations and show that, depending on the sign
of the initial perturbation, the solitons either collapse to a Schwarzschild
black hole or else ``explode'' into an outward moving domain wall.
