  We discuss the inclusion of running coupling effects in perturbative small x
evolution equations. We show that a running coupling BFKL-like x-evolution
equation is fully compatible, up to higher twist corrections, with the standard
factorized perturbative evolution of parton distributions. We then use this
result, combined with the well-known Airy asymptotics, to prove that the
oscillations which are present in the running-coupling BFKL solution do not
affect the associated splitting functions, which instead remain smooth in the
small x limit. This allows us to give a prescription to include
running-coupling corrections in the small-x resummation of scaling violations.
We show that these corrections are small in the HERA region.
