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

[11] SEMICLASSICAL ASYMPTOTIC APPROXIMATION OF THE TWO-DIMENSIONAL HARTREE OPERATOR SPECTRUM NEAR THE UPPER BOUNDARIES OF SPECTRAL CLUSTERS
Pereskokov, A. V.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2016, 187 (01) : 511 - 524
[12] Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters
Pereskokov, A. V.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2014, 178 (01) : 76 - 92
[13] Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters
A. V. Pereskokov
[J]. Theoretical and Mathematical Physics, 2014, 178 : 76 - 92
[14] ASYMPTOTICS OF THE HARTREE OPERATOR SPECTRUM NEAR THE UPPER BOUNDARIES OF SPECTRAL CLUSTERS: ASYMPTOTIC SOLUTIONS LOCALIZED NEAR A CIRCLE
Pereskokov, A. V.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2015, 183 (01) : 516 - 526
[15] Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle
A. V. Pereskokov
[J]. Theoretical and Mathematical Physics, 2015, 183 : 516 - 526
[16] Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators
Pereskokov, A. V.
[J]. MATHEMATICAL NOTES, 2012, 92 (3-4) : 532 - 543
[17] Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators
A. V. Pereskokov
[J]. Mathematical Notes, 2012, 92 : 532 - 543
[18] Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluster
A. V. Pereskokov
[J]. Theoretical and Mathematical Physics, 2020, 205 : 1652 - 1665
[19] Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluster
Pereskokov, A. V.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2020, 205 (03) : 1652 - 1665
[20] Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Lower Boundaries of Spectral Clusters
Pereskokov A.V.
[J]. Journal of Mathematical Sciences, 2021, 259 (2) : 244 - 263

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