  We solve numerically the Schwinger-Dyson (SD hereafter) ghost equation in the
Landau gauge for a given gluon propagator finite at k=0 (alpha_gluon=1) and
with the usual assumption of constancy of the ghost-gluon vertex ; we show that
there exist two possible types of ghost dressing function solutions, as we have
previously inferred from analytical considerations : one singular at zero
momentum, satisfying the familiar relation alpha_gluon+2 alpha_ghost=0 between
the infrared exponents of the gluon and ghost dressing functions(in short,
respectively alpha_G and alpha_F) and having therefore alpha_ghost=-1/2, and
another which is finite at the origin (alpha_ghost=0), which violates the
relation. It is most important that the type of solution which is realized
depends on the value of the coupling constant. There are regular ones for any
coupling below some value, while there is only one singular solution, obtained
only at a critical value of the coupling. For all momenta k<1.5 GeV where they
can be trusted, our lattice data exclude neatly the singular one, and agree
very well with the regular solution we obtain at a coupling constant compatible
with the bare lattice value.
