  The formalism of Ursell operators provides a self-consistent integral
equation for the one-particle reduced operator. In three dimensions this
technique yields values of the shift in the Bose-Einstein condensation (BEC)
transition temperature, as a function of the scattering length, that are in
good agreement with those of Green's function and quantum Monte Carlo methods.
We have applied the same equations to a uniform two-dimensional system and find
that, as we alter the chemical potential, an instability develops so that the
self-consistent equations no longer have a solution. This instability, which
seems to indicate that interactions restore a transition, occurs at a non-zero
value of an effective chemical potential. The non-linear equations are limited
to temperatures greater than or equal to Tc, so that they do not indicate the
nature of the new stable state, but we speculate concerning whether it is a
Kosterlitz-Thouless state or a ``smeared'' BEC, which might avoid any violation
of the Hohenberg theorem, as described in an accompanying paper.
