  Based on the Kaplan-Nelson Lagrangian, we investigate kaon condensation in
dense neutron star matter allowing for the explicit presence of hyperons. Using
various models we find that the condensate threshold is sensitive to the
behavior of the scalar density; the more rapidly it increases with baryon
density, the lower is the threshold for condensation. The presence of hyperons,
particularly the $\Sigma^-$, shifts the threshold for $K^-$ condensation to a
higher density. In the mean field approach, with hyperons, the condensate
amplitude grows sufficiently rapidly that the nucleon effective mass vanishes
at a finite density and a satisfactory treatment of the thermodynamics cannot
be achieved. Thus, calculations of kaon-baryon interactions beyond the mean
field level appear to be necessary.
