  We study Dyson-Schwinger equations for propagators of Dirac fermions
interacting with a massive gauge boson in the ladder approximation. The
equations have the form of the coupled nonlinear integral Fredholm equations of
the second kind in the spacelike domain. The solutions in the timelike domain
are completely defined by evaluations of integrals of the spacelike domain
solutions. We solve the equations and analyze the behavior of solutions on the
mass of the gauge boson, the coupling constant, and the ultraviolet cutoff. We
find that there are at least two solutions for the fixed gauge boson mass,
coupling, and the ultraviolet cutoff, thus there are at least two fermion
families. The zero-node solution represents the heaviest Dirac fermion state,
while the one-node solution is the lighter one. The mass gap between the two
families is of the order of magnitude observed in nature.
