  We derive simplified Faddeev type equations for the three particle T-matrix
which are valid in the Hubbard model where only electrons with opposite spins
interact. Using the approximation of dynamical mean field theory these
equations are partially solved numerically for the attractive Hubbard model. It
is shown that the three particle T-matrix contains a term vanishing $\sim T^2$
at the Thouless (or BCS) instability where the two-particle T-matrix diverges.
Based on the three particle term we further derive the low density - strong
coupling extension for the two-particle vertex function. We therefore
understand our equations as a step towards a systematic low density expansion
from the weak coupling BCS theory towards the stronger coupling limit.
