Geodesic
Asymptotics of the~spectrum of a Hartree-type operator with a~screened Coulomb self-action potential near the~upper boundaries of spectral clusters
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 543-560

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We consider the eigenvalue problem for a Hartree-type operator with a screened Coulomb self-action potential and with a small parameter multiplying the nonlinearity. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundaries of spectral clusters that form near the energy levels of the unperturbed operator.
Keywords: spectral cluster, self-consistent field, asymptotic eigenvalue, asymptotic eigenfunction, solvability condition. 
@article{TMF_2021_209_3_a8,
     author = {A. V. Pereskokov},
     title = {Asymptotics of the~spectrum of a {Hartree-type} operator with a~screened {Coulomb} self-action potential near the~upper boundaries of spectral clusters},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {543--560},
     publisher = {mathdoc},
     volume = {209},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a8/}
}
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A. V. Pereskokov. Asymptotics of the~spectrum of a Hartree-type operator with a~screened Coulomb self-action potential near the~upper boundaries of spectral clusters. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 543-560. http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a8/