A. V. Pereskokov, “Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluste”, TMF, 2020, Volume 205, Number 3,Pages <nobr>467

This article is cited in 2 papers

Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluste

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 the two-dimensional Hartree operator with a small nonlinearity coefficient. We find the asymptotic eigenvalues and asymptotic eigenfunctions near a local maximum of the eigenvalues in spectral clusters formed near the eigenvalues of the unperturbed operator.

Keywords: spectral cluster, WKB approximation, asymptotic eigenvalue, asymptotic eigenfunction, logarithmic singularity.

Received: 13.05.2020
Revised: 31.07.2020

DOI: 10.4213/tmf9934