  Motivated by recent experiments on small radius nanotubes, we study the
superconducting instabilities of cylindrical (5,0) nanotubes. According to band
structure calculations, thesenanotubes possess three bands at the Fermi energy.
  Using a fermionic renormalization group approach and a careful bosonization
treatment,we consider the effect of different attractive interactions, mediated
by phonons, within the Luttinger Liquid framework. We particularly focus on a
superconducting instability specific to the three bands model we consider for
the description of these
  (5,0) cylindrical nanotubes.
