  We show that the Dyson-Schwinger set of equations for the Yang-Mills theory
can be exactly solved till the two-point function. This is obtained given a set
of nonlinear waves solving the classical equations of motion. Translation
invariance is maintained by the proper choice of the solution of the equation
for the two-point function as devised by Coleman. The computation of the
Dyson-Schwinger equations is performed in the same way as devised by Bender,
Milton and Savage providing a set of partial differential equations whose proof
of existence of the solutions is standard. So, the correlation functions of the
theory could be proved to exist and the two-point function manifests a mass
gap.
