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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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).
The author declares no conflicts of interest.
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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
- spectral cluster
- WKB approximation
- asymptotic eigenvalue
- asymptotic eigenfunction
- logarithmic singularity