A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters”, TMF, 2016, Volume 187, Number 1,Pages <nobr>74

This article is cited in 9 papers

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

A. V. Pereskokov^ab

^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.

Received: 06.07.2015
Revised: 21.11.2015

DOI: 10.4213/tmf9001