  We present the general derivation of the full non-perturbative equation that
governs the momentum evolution of the dynamically generated gluon mass, in the
Landau gauge. The entire construction hinges crucially on the inclusion of
longitudinally coupled vertices containing massless poles of non-perturbative
origin, which preserve the form of the fundamental Slavnov-Taylor identities of
the theory. The mass equation is obtained from a previously unexplored version
of the Schwinger-Dyson equation for the gluon propagator, particular to the
PT-BFM formalism, which involves a reduced number of "two-loop dressed"
diagrams, thus simplifying the calculational task considerably. The two-loop
contributions turn out to be of paramount importance, modifying the qualitative
features of the full mass equation, and enabling the emergence of physically
meaningful solutions. Specifically, the resulting homogeneous integral equation
is solved numerically, subject to certain approximations, for the entire range
of physical momenta, yielding positive-definite and monotonically decreasing
gluon masses.
