Email this article Semiclassical Asymptotics of Solutions to Hartree Type Equations Concentrated on Segments
- Authors: Pereskokov A.V.1,2
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Affiliations:
- National Research University “Moscow Power Engineering Institute”
- National Research University “Higher School of Economics”
- Issue: Vol 226, No 4 (2017)
- Pages: 462-516
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240006
- DOI: https://doi.org/10.1007/s10958-017-3544-8
- ID: 240006
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Abstract
We study the nonlinear eigenvalue problem for two-dimensional Hartree type equations with selfaction potentials possessing logarithmic singularity and depending on the distance between points. To find a series of asymptotic eigenvalues, we derive a counterpart of the Bohr–Sommerfeld quantization rule. The corresponding asymptotic eigenfunctions are localized near a plane segment.
About the authors
A. V. Pereskokov
National Research University “Moscow Power Engineering Institute”; National Research University “Higher School of Economics”
Author for correspondence.
Email: pereskokov62@mail.ru
Russian Federation, 14, Krasnokazarmennaya St., Moscow, 111250; 20, Myasnitskaya St., Moscow, 101978
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