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We present new spherically symmetric, dyonic soliton and black hole solutionsof the ${\mathfrak {su}}(N)$ Einstein-Yang-Mills equations in four-dimensionalasymptotically anti-de Sitter space-time. The gauge field has nontrivialelectric and magnetic components and is described by $N-1$ magnetic gauge fieldfunctions and $N-1$ electric gauge field functions. We explore the phase spaceof solutions in detail for ${\mathfrak {su}}(2)$ and ${\mathfrak {su}}(3)$gauge groups. Combinations of the electric gauge field functions are monotonicand have no zeros; in general the magnetic gauge field functions may havezeros. The phase space of solutions is extremely rich, and we find solutions inwhich the magnetic gauge field functions have more than fifty zeros. Ofparticular interest are solutions for which the magnetic gauge field functionshave no zeros, which exist when the negative cosmological constant hassufficiently large magnitude. We conjecture that at least some of thesenodeless solutions may be stable under linear, spherically symmetric,perturbations.

Dyons and dyonic black holes in ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory in anti-de Sitter space-time