Bifurcation of Solutions of Abstract Kinetic Equation

The present paper is dedicated for basic aspects of theory of branching of solutions of nonlinear operator equations of special kind (applying in physical kinetics). Iodification of Lyapunov-Schmidt construction, which uses mathematical apparatus of infinite-dimensional projectors, is carried out. The properties of evolution operator for solutions of above-mentioned equations are considered. The properties of bifurcation equations for ones are investigated.