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TMF, 2016, Volume 187, Number 1, Pages 74–87 (Mi tmf9001)  

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

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).


DOI: https://doi.org/10.4213/tmf9001

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English version:
Theoretical and Mathematical Physics, 2016, 187:1, 511–524

Bibliographic databases:

Received: 06.07.2015
Revised: 21.11.2015

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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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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