  The properties of kaonic nuclei are studied using a two-dimensional
Skyrme-Hartree-Fock model with a $KN$ Skyrme force. We focus in particular on
the instability of the solutions for a too strong $KN$ interaction, which
determines a maximum value of the kaon binding in this approach. We then
analyze the change of the deformation properties of several core-deformed
nuclei caused by the added kaon, and find a shrinking of the core and in some
cases a complete loss of deformation.
