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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 183, Number 1, Pages 78–89
DOI: https://doi.org/10.4213/tmf8761 (Mi tmf8761) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle

A. V. Pereskokovab

a Federal State Budget Educational Institution of Higher Professional Education National Research University "Moscow Power Engineering Institute" (MPEI), Moscow, Russia
b National Research University "Higher School of Economics" — Moscow Institute of Electronics and Mathematics, Moscow, Russia
Full-text PDF (432 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf8761
Abstract: We consider the eigenvalue problem for the Hartree operator with a small parameter multiplying the nonlinearity. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundaries of spectral clusters formed near the energy levels of the unperturbed operator. Near the circle where the solution is localized, the leading term of the expansion is a solution of the two-dimensional oscillator problem.
Keywords: self-consistent field, spectral cluster, asymptotic eigenvalue, asymptotic eigenfunction, two-dimensional oscillator, logarithmic singularity.
Funding agency Grant number
Russian Science Foundation 14-11-00306
Ministry of Education and Science of the Russian Federation НШ-2081.2014.1
Received: 01.07.2014
Revised: 25.09.2014
English version:
Theoretical and Mathematical Physics, 2015, Volume 183, Issue 1, Pages 516–526
DOI: https://doi.org/10.1007/s11232-015-0278-y
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Pereskokov, “Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle”, TMF, 183:1 (2015), 78–89; Theoret. and Math. Phys., 183:1 (2015), 516–526
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf8761
  • https://doi.org/10.4213/tmf8761
  • https://www.mathnet.ru/eng/tmf/v183/i1/p78
    • This publication is cited in the following 8 articles:
    1. A. V. Pereskokov, “Asymptotics of the Spectrum of a Threedimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters”, J Math Sci, 281:4 (2024), 612  crossref
    2. A. V. Pereskokov, “Asymptotic Solutions to the Hartree Equation Near a Sphere. Asymptotics of Self-Consistent Potentials”, J Math Sci, 276:1 (2023), 154  crossref
    3. A. V. Pereskokov, “Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters”, Theoret. and Math. Phys., 209:3 (2021), 1782–1797  mathnet  crossref  crossref  adsnasa  isi  elib
    4. A. V. Pereskokov, “Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluste”, Theoret. and Math. Phys., 205:3 (2020), 1652–1665  mathnet  crossref  crossref  adsnasa  isi  elib
    5. D. A. Vakhrameeva, A. V. Pereskokov, “Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters”, Theoret. and Math. Phys., 199:3 (2019), 864–877  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. A. V. Pereskokov, “Semiclassical Asymptotics of Solutions to Hartree Type Equations Concentrated on Segments”, J Math Sci, 226:4 (2017), 462  crossref
    7. A. V. Pereskokov, “Asymptotics of the Spectrum of a Two-dimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters. Asymptotic Solutions Located Near a Circle”, J Math Sci, 226:4 (2017), 517  crossref
    8. A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters”, Theoret. and Math. Phys., 187:1 (2016), 511–524  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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