  A truncated BFKL series is studied and applied to hadronic processes. The
proton-(anti)proton cross sections are described with good agreement with data
and in a way consistent with the unitarity bound. The elastic scattering
amplitude is calculated at momentum transfer $t$ different from zero,
introducing two distinct ansatze for the proton impact factor. The elastic
differential cross section is obtained at small $t$ approximation and compared
with the data.
