  We use the quasistatic approach to analyze the criterion of ferromagnetism
for two-dimensional (2D) systems with the Fermi level near Van Hove
singularities (VHS) of the electronic spectrum. It is shown that the spectrum
of spin excitations (paramagnons) is positively defined when the interaction I
between electrons and paramagnons, which corresponds to the Hubbard on-site
repulsion U, is sufficiently large. The critical interactions I_c and U_c
remain finite at Van Hove filling and exceed considerably their values obtained
from the Stoner criterion due to incommensurate spin fluctuations which are
important near the ferromagnetic quantum phase transition. Combining the
quasistatic approximation and the equation-of -motion method for the Green
functions we obtain the results for the electronic self-energy to first order
in the inverse number of spin components.
