Asymptotics of The Spectrum of a Two-Dimensional Hartree-Type Operator with a Coulomb Self-Action Potential Near the Lower Boundaries of Spectral Clusters

被引：0

作者：

D. A. Vakhrameeva

A. V. Pereskokov

机构：

[1] National Research University Higher School of Economics,

[2] Federal State Budget Educational Institution of Higher Education National Research University Moscow Power Engineering Institute,undefined

来源：

Theoretical and Mathematical Physics | 2019年 / 199卷

关键词：

self-consistent field; spectral cluster; spectrum splitting; asymptotic eigenvalue; asymptotic eigenfunction;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：864 / 877

页数：13

共 24 条

[1] ASYMPTOTICS OF THE SPECTRUM OF A TWO-DIMENSIONAL HARTREE-TYPE OPERATOR WITH A COULOMB SELF-ACTION POTENTIAL NEAR THE LOWER BOUNDARIES OF SPECTRAL CLUSTERS
Vakhrameeva, D. A.
Pereskokov, A., V
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2019, 199 (03) : 864 - 877
[2] 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
[J]. Theoretical and Mathematical Physics, 2021, 209 : 1782 - 1797
[3] Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters
Pereskokov, A., V
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2021, 209 (03) : 1782 - 1797
[4] Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters
Pereskokov, Alexander
[J]. APPLICABLE ANALYSIS, 2016, 95 (07) : 1560 - 1569
[5] Semiclassical Asymptotics of the Spectrum of a Two-Dimensional Hartree Type Operator Near Boundaries of Spectral Clusters
Pereskokov A.V.
[J]. Journal of Mathematical Sciences, 2022, 264 (5) : 617 - 632
[6] Semiclassical asymptotics of the spectrum near the lower boundary of spectral clusters for a Hartree-type operator
A. V. Pereskokov
[J]. Mathematical Notes, 2017, 101 : 1009 - 1022
[7] Semiclassical asymptotics of the spectrum near the lower boundary of spectral clusters for a Hartree-type operator
Pereskokov, A. V.
[J]. MATHEMATICAL NOTES, 2017, 101 (5-6) : 1009 - 1022
[8] Asymptotics of the Spectrum and Quantum Averages of a Hartree Type Operator Near the Lower Boundaries of Spectral Clusters
Vakhrameeva D.A.
Pereskokov A.V.
[J]. Journal of Mathematical Sciences, 2020, 247 (6) : 820 - 849
[9] Asymptotics of the Spectrum of a Two-dimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters. Asymptotic Solutions Located Near a Circle
Pereskokov A.V.
[J]. Journal of Mathematical Sciences, 2017, 226 (4) : 517 - 530
[10] Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters
A. V. Pereskokov
[J]. Theoretical and Mathematical Physics, 2016, 187 : 511 - 524

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