  There is a wide-spread belief in the literature on Bose-Einstein condensation
of interacting atoms that all variants of mean-field theory incorrectly
describe the condensation phase transition, exhibiting, instead of the
necessary second-order transition, a first-order transition, even for weakly
interacting Bose gas. In the present paper, it is shown that a self-consistent
mean-field approach is the sole mean-field theory that provides the correct
second-order condensation transition for Bose systems with atomic interactions
of arbitrary strength, whether weak or strong.
