  Possible coexistence and/or competition of kaon condensation with hyperons
are investigated in hyperonic matter, where hyperons are mixed in the ground
state of neutron-star matter. The formulation is based on the effective chiral
Lagrangian for the kaon-baryon interaction and the nonrelativistic
baryon-baryon interaction model. First, the onset condition of the s-wave kaon
condensation realized from hyperonic matter is reexamined. It is shown that the
usual assumption of the continuous phase transition is not always kept valid in
the presence of the negatively charged hyperons. Second, the equation of state
(EOS) of the kaon-condensed phase in hyperonic matter is discussed. In the case
of the stronger kaon-baryon attractive interaction, it is shown that a local
energy minimum with respect to the baryon number density appears as a result of
considerable softening of the EOS due to both kaon condensation and
hyperon-mixing and recovering of the stiffness of the EOS at very high
densities. This result implies a possible existence of self-bound objects with
kaon condensates on any scale from an atomic nucleus to a neutron star.
