  We study the evolution of Born-Infeld-type phantom in the second
Randall-Sundrum brane scenario, and find that there exists attractor solution
for the potential with a maximum, which implies a cosmological constant at the
late time. Especially, we discuss the BI model of constant potential without
and with dust matter. In the weak tension limit of the brane, we obtain an
exact solution for the BI phantom and scale factor and show that there is no
big rip during the evolution of the brane.
