Some properties of evolution equation for homogeneous nucleation period   under the smooth behavior of initial conditions
  The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated equation have been established. On the base of these facts taking into account some properties of behavior of solution the uniqueness of the equation appeared in the theory of homogeneous nucleation has been established. The equivalence of auxiliary problem and the real problem is shown. 
Victor Kurasov