Cauchy problem for the Bogolyubov (BBGKY) equations. The BCS model

The Bogoliubov hierarchy of kinetic equations for infinite quantum system of particles distributed in space with mean density $1/v$ and interacting with the model operator of Bardeen–Cooper–Schrieffer, is treated as single abstract equation in a certain countably normed space $b^v$ of sequences of integral operators. The unique solution of the Gauchy problem with arbitrary initial conditions from $b^v$ is obtained, stationary solutions of the equation are constructed and the class of initial conditions is pointed out which approach the stationary solutions in the process of the evolution.