  We study open strings in the noncritical $c=1$ bosonic string theory
compactified on a circle at self-dual radius. These strings live on D-branes
that are extended along the Liouville direction ({\it FZZT} branes). We present
explicit expressions for the disc two- and three-point functions of boundary
operators in this theory, as well as the bulk-boundary two-point function. The
expressions obtained are divergent because of resonant behaviour at self-dual
radius. However, these can be regularised and renormalized in a precise way to
get finite results. The boundary correlators are found to depend only on the
differences of boundary cosmological constants, suggesting a fermionic
behaviour. We initiate a study of the open-string field theory localised to the
physical states, which leads to an interesting matrix model.
