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We determine the properties of kaonic (K-) nuclei in the Skyrme–Hartree–Fock nuclear structure approach. We use a standard chiral model with adjustable interaction strength for the kaon–nucleon interaction. The sensitivity to details of the nuclear Skyrme force, in particular, the nuclear compressibility, is studied. We find instabilities for a too strong kaon–nucleon interaction, which effectively limits the maximum binding of the kaon in this approach.