  A solution to the cosmological constant problem has been proposed in which
our universe is a 3-brane in a 5-dimensional spacetime. With a bulk scalar, the
field equations admit a Poincare invariant brane solution regardless of the
value of the cosmological constant (tension) on the brane. However, the
solution does not include matter in the brane. We find new exact static
solutions with matter density and pressure in the brane. We study small
perturbations about these solutions. None seem consistent with observational
cosmology. As a byproduct we find a class of new matterless static solutions
and a non-static solution which, curiously, requires the string value for the
dilaton coupling.
