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TMF, 2019, Volume 199, Number 3, Pages 445–459 (Mi tmf9664)  

Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters

D. A. Vakhrameevaa, A. V. Pereskokovba

a National Research University Higher School of Economics, Moscow, Russia
b Federal State Budget Educational Institution of Higher Education National Research University Moscow Power Engineering Institute, Moscow, Russia

Abstract: We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where the solution is localized.

Keywords: self-consistent field, spectral cluster, spectrum splitting, asymptotic eigenvalue, asymptotic eigenfunction.

Funding Agency Grant Number
National Research University Higher School of Economics
Russian Science Foundation 19-11-00033
The research of D. A. Vakhrameeva is supported by the Program of Fundamental Research of the National Research University Higher School of Economics.
The research of A. V. Pereskokov is supported by a grant from the Russian Science Foundation (Project No. 19-11-00033).


DOI: https://doi.org/10.4213/tmf9664

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English version:
Theoretical and Mathematical Physics, 2019, 199:3, 864–877

Bibliographic databases:

Received: 08.12.2018
Revised: 23.01.2019

Citation: D. A. Vakhrameeva, A. V. Pereskokov, “Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters”, TMF, 199:3 (2019), 445–459; Theoret. and Math. Phys., 199:3 (2019), 864–877

Citation in format AMSBIB
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