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Semiclassical Asymptotics of the Spectrum of a Two-Dimensional Hartree Type Operator Near Boundaries of Spectral Clusters

Journal of Mathematical Sciences. 2022. Vol. 264. No. 5. P. 617–632.
Pereskokov A.

We consider the spectral problem for a perturbed two-dimensional oscillator. The role of a perturbation is played by an integral Hartree type nonlinearity with a self-action potential depending on the distance between points and possessing a Coulomb singularity. We find asymptotic eigenvalues and eigenfunctions near boundaries of spectral clusters appearing near eigenvalues of the unperturbed operator. we construct an asymptotic expansion near a circle, where the solution is located. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Research target: Mathematics
Language: English
Full text
DOI
Keywords: спектральный кластерasymptotic eigenvalues and eigenfunctionsасимптотические собственные значения и собственные функциисамосогласованное полеself-consistent fieldдвумерный осцилляторspectral clustertwo-dimensional oscillator
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