  We study quantum chromodynamics from the viewpoint of untruncated
Dyson-Schwinger equations turned to an ordinary differential equation for the
gluon anomalous dimension. This nonlinear equation is parameterized by a
function P(x) which is unknown beyond perturbation theory. Still, very mild
assumptions on P(x) lead to stringent restrictions for possible solutions to
Dyson-Schwinger equations. We establish that the theory must have asymptotic
freedom beyond perturbation theory and also investigate the low energy regime
and the possibility for a mass gap in the asymptotically free theory.
