Geodesic
Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 74-87 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an eigenvalue problem for the two-dimensional Hartree operator with a small parameter at the nonlinearity. We obtain the asymptotic eigenvalues and the asymptotic eigenfunctions near the upper boundaries of the spectral clusters formed near the energy levels of the unperturbed operator and construct an asymptotic expansion around the circle where the solution is localized.
Keywords: self-consistent field, spectral cluster, asymptotic eigenvalue, asymptotic eigenfunction, logarithmic singularity. 
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     author = {A. V. Pereskokov},
     title = {Semiclassical asymptotic approximation of the~two-dimensional {Hartree} operator spectrum near the~upper boundaries of spectral clusters},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a5/}
}
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A. V. Pereskokov. Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 74-87. http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a5/

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