  A numerical study of the ghost Dyson-Schwinger equation in Coulomb gauge is
performed and solutions for the ghost propagator found. As input, lattice
results for the spatial gluon propagator are used. It is shown that in order to
solve completely, the equation must be supplemented by a nonperturbative
boundary condition (the value of the inverse ghost propagator dressing function
at zero momentum) which determines if the solution is critical (zero value for
the boundary condition) or subcritical (finite value). The various solutions
exhibit a characteristic behavior where all curves follow the same (critical)
solution when going from high to low momenta until `forced' to freeze out in
the infrared to the value of the boundary condition. The renormalization is
shown to be largely independent of the boundary condition. The boundary
condition and the pattern of the solutions can be interpreted in terms of the
Gribov gauge-fixing ambiguity. The connection to the temporal gluon propagator
and the infrared slavery picture of confinement is explored.
