Geodesic
Semiclassical asymptotic spectrum of the~two-dimensional Hartree operator near a~local maximum of the~eigenvalues in a~spectral cluste
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 467-483

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We consider the eigenvalue problem for the two-dimensional Hartree operator with a small nonlinearity coefficient. We find the asymptotic eigenvalues and asymptotic eigenfunctions near a local maximum of the eigenvalues in spectral clusters formed near the eigenvalues of the unperturbed operator.
Keywords: spectral cluster, WKB approximation, asymptotic eigenvalue, asymptotic eigenfunction, logarithmic singularity. 
@article{TMF_2020_205_3_a6,
     author = {A. V. Pereskokov},
     title = {Semiclassical asymptotic spectrum of the~two-dimensional {Hartree} operator near a~local maximum of the~eigenvalues in a~spectral cluste},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {467--483},
     publisher = {mathdoc},
     volume = {205},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a6/}
}
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A. V. Pereskokov. Semiclassical asymptotic spectrum of the~two-dimensional Hartree operator near a~local maximum of the~eigenvalues in a~spectral cluste. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 467-483. http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a6/