  We construct hairy static black holes of higher dimensional general coupling
Einstein-Skyrme theories with the scalar potential turned on and the
cosmological constant is non-positive in which the scalar multiplets satisfy
$O(d+1)$ model constraint where $d$ is the spatial dimension of the spacetime
and $d \ge 3$. Some physical properties of solutions near the boundaries,
namely, near the (event) horizon and in the asymptotic region are discussed.
Then, we prove that these black hole solutions exist globally which may have
finite energy for non-positive cosmological constant. Finally, we use
perturbative method to perform a linear dynamical stability analysis and then,
show the existence of stable and unstable solutions in the model.
