  We examine the possibility of Bose-Einstein condensation (BEC) in
two-dimensional (2D) system of interacting particles in a trap. We use a
self-consistent mean-field theory of Bose particles interacting by a contact
interaction in the Popov and WKB approximations. The equations show that the
normal state has a phase transition at some critical temperature (T_{c}) but
below (T_{c}) the Bose-Einstein condensed state is not a consistent solution of
the equations in the thermodynamic limit. This result agrees with a theorem
recently discussed by the author that shows that a BEC state is impossible for
an interacting gas in a 2D trap in the thermodynamic limit.
