Asymptotics of the Spectrum of a Two-dimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters. Asymptotic Solutions Located Near a Circle

被引：0

作者：

Pereskokov A.V. ^{[1
,2
]}

机构：

[1] National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya St, Moscow

[2] National Research University “Higher School of Economics”, 20, Myasnitskaya St, Moscow

来源：

Journal of Mathematical Sciences | 2017年 / 226卷 / 4期

基金：

俄罗斯科学基金会;

关键词：

D O I：

10.1007/s10958-017-3545-7

中图分类号：

学科分类号：

摘要：

We consider the eigenvalue problem for a two-dimensional perturbed resonance oscillator. The role of perturbation is played by an integral Hartree type nonlinearity, where the selfaction potential depends on the distance between points and has logarithmic singularity. We obtain asymptotic eigenvalues near the upper boundaries of spectral clusters appeared near eigenvalues of the unperturbed operator. © 2017, Springer Science+Business Media, LLC.

引用

页码：517 / 530

页数：13

共 31 条

[21] On the Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields Near the Upper Boundaries of Spectral Clusters
A. V. Pereskokov
[J]. Russian Journal of Mathematical Physics, 2019, 26 : 391 - 400
[22] On the Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields Near the Upper Boundaries of Spectral Clusters
Pereskokov, A. V.
[J]. RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2019, 26 (03) : 391 - 400
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[24] Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Lower Boundaries of Spectral Clusters
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[J]. Journal of Mathematical Sciences, 2021, 259 (2) : 244 - 263
[25] New type of semiclassical asymptotics of eigenstates near the boundaries of spectral clusters for Schrodinger-type operators
Pereskokov, Alexander V.
[J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DAYS ON DIFFRACTION 2016 (DD), 2016, : 323 - 326
[26] Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters
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[27] Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters
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[J]. MATHEMATICAL NOTES, 2020, 107 (5-6) : 804 - 819
[28] Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments
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[J]. Theoretical and Mathematical Physics, 2002, 131 : 775 - 790
[29] Asymptotic solutions of two-dimensional Hartree-type equations localized in the neighborhood of line segments
Pereskokov, AV
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2002, 131 (03) : 775 - 790
[30] Asymptotic solution to the Dirichlet problem for a two-dimensional Riccatti's type equation near a corner point
Maz'ya, V
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[J]. ASYMPTOTIC ANALYSIS, 2004, 39 (02) : 169 - 185

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