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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 1, Pages 74–87
DOI: https://doi.org/10.4213/tmf9001 (Mi tmf9001) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters

A. V. Pereskokovab

a National Research University Higher School of Economics — Moscow Institute of Electronics and Mathematics, Moscow, Russia
b State Budget Institution of Higher Professional Education National Research University MPEI, Moscow, Russia
Full-text PDF (440 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf9001
Abstract: 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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.756.2014/К
This research was performed in the framework of the governmental target program of the Russian Federation Ministry of Education and Science (Contract No. 1.756.2014/K).
Received: 06.07.2015
Revised: 21.11.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 1, Pages 511–524
DOI: https://doi.org/10.1134/S0040577916040061
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters”, TMF, 187:1 (2016), 74–87; Theoret. and Math. Phys., 187:1 (2016), 511–524
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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