Bifurcation in Poly-Parameter Operator Families and Kinetic Equations

In the present paper bifurcation in families of non-Fredholm Frechet-analytic mappings in Banach spaces (increasing of dimension of their null-spaces) is considered. Operators of this kind (as associated with Boltzmann or Ueling-Uhlenbeck equations) are applied in problems of physical kinetics. In connection with non-closedness of these operators ranges the modification of Lyapunov-Schmidt method of obtaining of 'bifurcation equation' (not algebraic) is carried out. The basic result of paper is Theorem 2 which gives methods ofexposure of bifurcation point in operator families with above-mentioned properties.