  We investigate supersymmetric extrema of Abelian gauged supergravity theories
with non-trivial vector multiplets and 8 supercharges in four and five
dimensions. The scalar fields of these models parameterize a manifold
consisting of disconnected branches and restricting to the case where this
manifold has a non-singular metric we show that on every branch there can be at
most one extremum, which is a local maximum (for W>0) or a minimum (for W<0) of
the superpotential W. Therefore, these supergravity models do not allow for
regular domain wall solutions interpolating between different extrema of the
superpotential and the space-time transverse to the wall asymptotically always
approaches the boundary of AdS (UV-fixed points in a dual field theory).
