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Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluster

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Abstract

We consider the eigenvalue problem for the two-dimensional Hartree operator with a small nonlinearity coefficient. We find the asymptotic eigenvalues and asymptotic eigenfunctions near a local maximum of the eigenvalues in spectral clusters formed near the eigenvalues of the unperturbed operator.

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Funding

This research was performed in the framework of a state task of the Ministry of Education and Science of the Russian Federation (Project No. FSWF-2020-0022).

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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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Pereskokov, A.V. Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluster. Theor Math Phys 205, 1652–1665 (2020). https://doi.org/10.1134/S0040577920120077

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  • DOI: https://doi.org/10.1134/S0040577920120077

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