  Schwinger-Dyson equations for propagators are solved for the scalar $\Phi^3$
theory and massive Wick-Cutkosky model.
  With the help of integral representation the results are obtained directly in
Minkowski space in and beyond bare vertex approximation. Various
renormalization scheme are employed which differ by the finite strength field
renormalization function $Z$ . The $S-$matrix is puzzled from the Green's
function and the effect of truncation of the DSEs is studied. Independently on
the approximation the numerical solution breaks down for certain critical value
of the coupling constant, for which the on-shell renormalized propagator starts
to develop the unphysical singularity at very high space-like square of
momenta.

High Energy Physics - Phenomenology