Geodesic
Cauchy problem for the Bogolyubov (BBGKY) equations. The BCS model
Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 1, pp. 49-59

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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. 
@article{TMF_1975_25_1_a6,
     author = {A. K. Vidybida},
     title = {Cauchy problem for the {Bogolyubov} {(BBGKY)} equations. {The} {BCS} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {49--59},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_25_1_a6/}
}
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A. K. Vidybida. Cauchy problem for the Bogolyubov (BBGKY) equations. The BCS model. Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 1, pp. 49-59. http://geodesic.mathdoc.fr/item/TMF_1975_25_1_a6/