  In this paper, we investigate the Einstein equations with cosmological
constant for Randall-Sundrum (RS) and Dvali-Gabadadze-Porrati (DGP) models to
determine the warp functions in the context of warp product spacetimes. In RS
model, it is shown that Einstein's equation in the bulk is reduced into the
brane as a vacuum equation, having vacuum solution, which is not affected by
the cosmological constant in the bulk. In DGP model, it is shown that the
Einstein's equation in the bulk is reduced into the brane and along the extra
dimension, where both equations are affected by the cosmological constant in
the bulk. We have solved these equations in DGP model, subject to vanishing
cosmological constants on the brane and along extra dimension, and obtained
exact solutions for the warp functions. The solutions depend on the typical
values of cosmological constant in the bulk as well as the dimension of the
brane. So, corresponding to the typical values, some solutions have exponential
behaviours which may be set to represent warp inflation on the brane, and some
other solutions have oscillating behaviours which may be set to represent warp
waves or branes waves along the extra dimension.
