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TMF, 2015, Volume 183, Number 1, Pages 78–89 (Mi tmf8761)  

This article is cited in 2 scientific papers (total in 2 papers)

Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle

A. V. Pereskokovab

a Federal State Budget Educational Institution of Higher Professional Education National Research University "Moscow Power Engineering Institute" (MPEI), Moscow, Russia
b National Research University "Higher School of Economics" — Moscow Institute of Electronics and Mathematics, Moscow, Russia

Abstract: We consider the eigenvalue problem for the Hartree operator with a small parameter multiplying the nonlinearity. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundaries of spectral clusters formed near the energy levels of the unperturbed operator. Near the circle where the solution is localized, the leading term of the expansion is a solution of the two-dimensional oscillator problem.

Keywords: self-consistent field, spectral cluster, asymptotic eigenvalue, asymptotic eigenfunction, two-dimensional oscillator, logarithmic singularity

Funding Agency Grant Number
Russian Science Foundation 14-11-00306
Ministry of Education and Science of the Russian Federation НШ-2081.2014.1


DOI: https://doi.org/10.4213/tmf8761

Full text: PDF file (432 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 183:1, 516–526

Bibliographic databases:

Received: 01.07.2014
Revised: 25.09.2014

Citation: A. V. Pereskokov, “Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle”, TMF, 183:1 (2015), 78–89; Theoret. and Math. Phys., 183:1 (2015), 516–526

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v183/i1/p78

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters”, Theoret. and Math. Phys., 187:1 (2016), 511–524  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. 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”, Theoret. and Math. Phys., 199:3 (2019), 864–877  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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