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Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters

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Abstract

We consider the eigenvalue problem for a Hartree-type operator with a screened Coulomb self-action potential and with a small parameter multiplying the nonlinearity. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundaries of spectral clusters that form near the energy levels of the unperturbed operator.

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Acknowledgments

The author thanks D. A. Vakhrameeva for the useful discussions of the results in this paper.

Funding

The work is supported by the Russian Science Foundation (Grant No. 19-11-00033).

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Authors and Affiliations

  1. National Research University “Higher School of Economics”, Moscow, Russia

    A. V. Pereskokov

  2. National Research University “Moscow Power Engineering Institute”, Moscow, Russia

    A. V. Pereskokov

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  1. A. V. Pereskokov
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Correspondence to A. V. Pereskokov.

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The author declares no conflicts of interest.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 209, pp. 543–560 https://doi.org/10.4213/tmf10127.

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Pereskokov, A.V. Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters. Theor Math Phys 209, 1782–1797 (2021). https://doi.org/10.1134/S0040577921120096

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  • DOI: https://doi.org/10.1134/S0040577921120096

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