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We consider black holes in EYM theory with a negative cosmological constant.The solutions obtained are somewhat different from those for which thecosmological constant is either positive or zero. Firstly, regular black holesolutions exist for continuous intervals of the parameter space, rather thandiscrete points. Secondly, there are non-trivial solutions in which the gaugefield has no nodes. We show that these solutions are linearly stable.Comment: 22 pages, 10 figures (1 ps file), LaTeX2e, uses amssymb, graphicx  Minor changes, version to appear in Classical and Quantum Gravit

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