Asymptotics of the Spectrum of a Two-dimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters. Asymptotic Solutions Located Near a Circle

Asymptotics of the Spectrum of a Two-dimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters. Asymptotic Solutions Located Near a Circle

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 eigenvalue...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-10, Vol.226 (4), p.517-530
1. Verfasser: Pereskokov, A. V.
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Boundaries
Clusters
Eigenvalues
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Zusammenfassung: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-017-3545-7