  The Friedmann-Robertson-Walker metric with spherical topology is calculated
as an effective metric at the brane in a multiple branes in $D-$dimensional
spacetime scenario. In this model the radius of the brane is the cosmological
scale factor, and its evolution is calculated from the viewpoint of the
observers on their respective branes. The cosmology of the brane-universe is
analyzed in cases where the anisotropic pressure has a cosmological constant
like state equation. The pressure values needed to distinguish the oscillating,
expanding or collapsing solutions are found, and the minimum value of a
brane-universe mass to prevent a collapse into a black hole is also calculated.
Finally the equation of motion is solved numerically in order to illustrate the
different cosmological scenarios and to validate the analytical results.
