D. A. Vakhrameeva, A. V. Pereskokov, “Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters”, TMF, 2019, Volume 199, Number 3,Pages <nobr>445

This article is cited in 3 papers

Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters

D. A. Vakhrameeva^a, A. V. Pereskokov^ba

^a National Research University Higher School of Economics, Moscow, Russia
^b Federal State Budget Educational Institution of Higher Education National Research University Moscow Power Engineering Institute, Moscow, Russia

Abstract: We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where the solution is localized.

Keywords: self-consistent field, spectral cluster, spectrum splitting, asymptotic eigenvalue, asymptotic eigenfunction.

Received: 08.12.2018
Revised: 23.01.2019

DOI: 10.4213/tmf9664