  Superconductivity in the quasi-one-dimensional material
Li$_{0.9}$Mo$_6$O$_{17}$ is analyzed based on a multiorbital extended Hubbard
model. We found strong charge fluctuations at two different momenta ${\bf Q_1}$
and ${\bf Q_2}$ giving rise to two different charge ordered phases. Evaluating
the superconducting vertex, we found superconductivity near strong charge
fluctuations at ${\bf Q_1}$. The order parameter has the p-wave symmetry with
nodes on the Fermi surface. The metallic state displays a characteristic charge
collective mode ${\bf Q_1}$ due to nesting and for on-site Hubbard repulsion
sufficiently large, a charge critical mode ${\bf Q_2}$ driven by Coulomb
repulsion, which softens at the proximity to the transition. The results are
quite robust for different coupling parametrizations. A phase diagram
discussing the relevance of the model to the physics of the material is
proposed.
