  We derived solutions for the Smoluchowski kinetic equation for the mass
function of galaxies, which describes mergers in differential approximation,
where mergers with low-mass galaxies are the dominant factor. The evolution of
the initial distribution is analyzed as well as the influence of the source
represented by galaxies (halos) that separate from the global cosmological
expansion. It is shown that the evolution of the slope of the power-law part of
the luminosity function at a constant mass-to-luminosity ratio observed in the
Ultra Deep Hubble Field can be described as a result of explosive evolution
driven by galaxy mergers. In this case the exponent depends exclusively on the
uniformity degree of merger probability as a function of mass.
