We consider the spectral problem for a perturbed two-dimensional oscillator. The role of a perturbation is played by an integral Hartree type nonlinearity with a self-action potential depending on the distance between points and possessing a Coulomb singularity. We find asymptotic eigenvalues and eigenfunctions near boundaries of spectral clusters appearing near eigenvalues of the unperturbed operator. we construct an asymptotic expansion near a circle, where the solution is located.
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Translated from Problemy Matematicheskogo Analiza 116, 2022, pp. 119-133.
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Pereskokov, A.V. Semiclassical Asymptotics of the Spectrum of a Two-Dimensional Hartree Type Operator Near Boundaries of Spectral Clusters. J Math Sci 264, 617–632 (2022). https://doi.org/10.1007/s10958-022-06021-5
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DOI: https://doi.org/10.1007/s10958-022-06021-5