  With a method in which the Friedmann equation is written in a form such that
evolution of the scale factor can be treated as that of a particle in a
"potential", we classify all possible cosmic evolutions in the DGP braneworld
scenario with the dark radiation term retained. By assuming that the energy
component is pressureless matter, radiation or vacuum energy, respectively, we
find that in the matter or vacuum energy dominated case, the scale factor has a
minimum value $a_0$. In the matter dominated case, the big bang singularity can
be avoided in some special circumstances, and there may exist an oscillating
universe or a bouncing one. If the cosmic scale factor is in the oscillating
region initially, the universe may undergo an oscillation. After a number of
oscillations, it may evolve to the bounce point through quantum tunneling and
then expand. However, if the universe contracts initially from an infinite
scale, it can turn around and then expand forever. In the vacuum energy
dominated case, there exists a stable Einstein static state to avoid the big
bang singularity. However, in certain circumstances in the matter or vacuum
energy dominated case, a new kind of singularity may occur at $a_0$ as a result
of the discontinuity of the scale factor. In the radiation dominated case, the
universe may originate from the big bang singularity, but a bouncing universe
which avoids this singularity is also possible.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics