  The Dvali, Gabadadze and Porrati (DGP) model has a self-accelerating
solution, the positive branch, where the brane is asymptotically de Sitter. A
de Sitter space-time can be seen as a boundary between quintessence-like
behaviour and phantom-like behaviour. We show that in a 5D dilatonic bulk,
where the dilaton has an exponential potential, with an induced gravity term on
the brane, whose matter content corresponds only to vacuum energy, the positive
branch solution undergoes a phantom-like stage where it faces a curvature
singularity in its infinite future. The singularity can be interpreted as the
``big rip'' singularity pushed towards an infinite future cosmic time. The
phantom-like behaviour on the brane occurs without violating the null energy
condition. There is another solution, the negative branch, where the brane can
undergo an early-epoch (transient) inflationary phase induced by the dilaton
field.
