Email this article Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters
- Authors: Pereskokov A.V.1,2
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Affiliations:
- Federal State Budget Institution of Higher Professional Education National Research University MPEI
- National Research University Higher School of Economics–Moscow Institute of Electronics and Mathematics
- Issue: Vol 187, No 1 (2016)
- Pages: 511-524
- Section: Article
- URL: https://journals.rcsi.science/0040-5779/article/view/170521
- DOI: https://doi.org/10.1134/S0040577916040061
- ID: 170521
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Abstract
We consider an eigenvalue problem for the two-dimensional Hartree operator with a small parameter at the nonlinearity. We obtain the asymptotic eigenvalues and the asymptotic eigenfunctions near the upper boundaries of the spectral clusters formed near the energy levels of the unperturbed operator and construct an asymptotic expansion around the circle where the solution is localized.
About the authors
A. V. Pereskokov
Federal State Budget Institution of Higher Professional Education National Research University MPEI; National Research University Higher School of Economics–Moscow Institute of Electronics and Mathematics
Author for correspondence.
Email: pereskokov62@mail.ru
Russian Federation, Moscow; Moscow
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