  We study a system of fermions interacting with a scalar field, in 4+1
dimensions where the 5th dimension is compactified, using an exact functional
method, where quantum fluctuations are controlled by the amplitude of the bare
fermion mass. The integration of our equationsleads to the properties of the
dressed Yukawa coupling, that we study at one-loop so as to show the
consistency of the approach. Beyond one loop, the non-perturbative aspect of
the method gives us the possibility to derive the dynamical fermion mass. The
result obtained is cut off independent and this derivation proposes an
alternative to the Schwinger-Dyson approach.
