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September 17, 2026
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Asymptotics of the spectrum of a two-dimensional Hartree type operator near upper boundaries of spectral clusters. Asymptotic solutions located near a circle

Journal of Mathematical Sciences. 2017. Vol. 226. No. 4. P. 517–530.
A. V. Pereskokov

We consider the eigenvalue problem for a two-dimensional perturbed resonance oscillator. The role of perturbation is played by an integral Hartree type nonlinearity, where the selfaction potential depends on the distance between points and has logarithmic singularity. We obtain asymptotic eigenvalues near the upper boundaries of spectral clusters appeared near eigenvalues of the unperturbed operator.

Research target: Physics Mathematics
Priority areas: mathematics
Language: English
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DOI
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Keywords: спектральный кластерasymptotic eigenvalues and eigenfunctionsасимптотические собственные значения и собственные функциивозмущенный осцилляторлогарифмическая особенностьlogarithmic singularityspectral clusterHartree type nonlinearityperturbed oscillatorнелинейность типа Хартри
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