  We construct solutions of an Einstein-Yang-Mills system including a
cosmological constant in 4+n space-time dimensions, where the n-dimensional
manifold associated with the extra dimensions is taken to be Ricci flat.
Assuming the matter and metric fields to be independent of the n extra
coordinates, a spherical symmetric Ansatz for the fields leads to a set of
coupled ordinary differential equations. We find that for n > 1 only solutions
with either one non-zero Higgs field or with all Higgs fields constant and zero
gauge fields exist. We give the analytic solutions available in this model.
These are ``embedded'' abelian solutions with a diverging size of the manifold
associated with the extra n dimensions. Depending on the choice of parameters,
these latter solutions either represent naked singularities or they possess a
single horizon.
  We also present solutions of the effective 4-dimensional
Einstein-Yang-Mills-Higgs-dilaton model, where the higher dimensional
cosmological constant induces a Liouville-type potential. The solutions are
non-abelian solutions with diverging Higgs fields, which exist only up to a
maximal value of the cosmological constant.
