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

[1] 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
[2] 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
[3] 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
[4] 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
[5] 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
[6] Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters
Pereskokov, Alexander
[J]. APPLICABLE ANALYSIS, 2016, 95 (07) : 1560 - 1569
[7] 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
[8] 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
[9] Asymptotics of The Spectrum of a Two-Dimensional Hartree-Type Operator with a Coulomb Self-Action Potential Near the Lower Boundaries of Spectral Clusters
D. A. Vakhrameeva
A. V. Pereskokov
[J]. Theoretical and Mathematical Physics, 2019, 199 : 864 - 877
[10] 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

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