Semiclassical asymptotics of solutions to Hartree type equations concentrated on segments

DOI10.1007/s10958-017-3544-8zbMath1390.81178OpenAlexW2754589875MaRDI QIDQ1688475

A. V. Pereskokov

Publication date: 8 January 2018

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-017-3544-8

zbMATH Keywords

nonlinear eigenvalue problemlogarithmic singularityasymptotic eigenfunctionsHartree type equationselfacton potential

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (1)

Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters

Cites Work

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• Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters
• Asymptotic solutions of two-dimensional Hartree-type equations localized in the neighborhood of line segments
• Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: asymptotic solutions localized near a circle
• Semiclassical asymptotics of the spectrum near the lower boundary of spectral clusters for a Hartree-type operator
• Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters
• Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. II. Localization in planar discs
• Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. I. The model with logarithmic singularity

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