  Inflationary solutions are constructed in a specific five-dimensional model
with boundaries motivated by heterotic M-theory. We concentrate on the case
where the vacuum energy is provided by potentials on those boundaries. It is
pointed out that the presence of such potentials necessarily excites bulk
Kaluza-Klein modes. We distinguish a linear and a non-linear regime for those
modes. In the linear regime, inflation can be discussed in an effective
four-dimensional theory in the conventional way. We lift a four-dimensional
inflating solution up to five dimensions where it represents an inflating
domain wall pair. This shows explicitly the inhomogeneity in the fifth
dimension. We also demonstrate the existence of inflating solutions with
unconventional properties in the non-linear regime. Specifically, we find
solutions with and without an horizon between the two boundaries. These
solutions have certain problems associated with the stability of the additional
dimension and the persistence of initial excitations of the Kaluza-Klein modes.
