  The dielectric function method for superconductivity has been applied to
SrTiO$_{3}$ accounting for the non-parabolic dispersion of charge carriers in
the conduction band and for the dispersion of optical phonons based on density
functional theory calculations. The obtained critical temperatures of the
superconducting phase transition in SrTiO$_{3}$ are in agreement with
experiments in the density range $n\sim5\times10^{18}$ to $5\times10^{20}$
cm$^{-3}$. The dielectric function method predicts also the sign of the
anomalous isotope effect in strontium titanate, in line with recent
observations.
