A. V. Pereskokov, “Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle”, TMF, 2015, Volume 183, Number 1,Pages <nobr>78

This article is cited in 8 papers

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

A. V. Pereskokov^ab

^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.

Received: 01.07.2014
Revised: 25.09.2014

DOI: 10.4213/tmf8761