Existence of stable hairy black holes in su(2) Einstein-Yang-Mills theory with a negative cosmological constant

We consider black holes in EYM theory with a negative cosmolo gical constant. The solutions obtained are somewhat different fro m those for which the cosmological constant is either positive or zero. First ly, regular black hole solutions exist for continuous intervals of the parameter s pace, rather than discrete points. Secondly, there are non-trivial solution s in which the gauge field has no nodes. We show that these solutions are linearly s table.