  We have performed self-consistent calculations of the nonlinear screening of
a point charge Z in a two-dimensional electron gas using a density functional
theory method. We find that the screened potential for a Z=1 charge supports a
bound state even in the high density limit where one might expect perturbation
theory to apply. To explain this behaviour, we prove a theorem to show that the
results of linear response theory are in fact correct even though bound states
exist.
