A. V. Pereskokov, “Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters”, TMF, 2021, Volume 209, Number 3,Pages <nobr>543

This article is cited in 1 paper

Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters

A. V. Pereskokov^ab

^a National Research University "Higher School of Economics", Moscow, Russia
^b National Research University "Moscow Power Engineering Institute", Moscow, Russia

Abstract: We consider the eigenvalue problem for a Hartree-type operator with a screened Coulomb self-action potential and with a small parameter multiplying the nonlinearity. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundaries of spectral clusters that form near the energy levels of the unperturbed operator.

Keywords: spectral cluster, self-consistent field, asymptotic eigenvalue, asymptotic eigenfunction, solvability condition.

Received: 14.05.2021
Revised: 20.08.2021

DOI: 10.4213/tmf10127