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Expansion of eigenvalues of the perturbed discrete bilaplacian

We consider the family [Formula: see text] of discrete Schrödinger-type operators in d-dimensional lattice [Formula: see text] , where [Formula: see text] is the discrete Laplacian and [Formula: see text] is of rank-one. We prove that there exist coupling constant thresholds [Formula: see text] such...

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Autores principales: Kholmatov, Shokhrukh Yu., Khalkhuzhaev, Ahmad, Pardabaev, Mardon
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Vienna 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8983584/
https://www.ncbi.nlm.nih.gov/pubmed/35464818
http://dx.doi.org/10.1007/s00605-022-01678-1
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author Kholmatov, Shokhrukh Yu.
Khalkhuzhaev, Ahmad
Pardabaev, Mardon
author_facet Kholmatov, Shokhrukh Yu.
Khalkhuzhaev, Ahmad
Pardabaev, Mardon
author_sort Kholmatov, Shokhrukh Yu.
collection PubMed
description We consider the family [Formula: see text] of discrete Schrödinger-type operators in d-dimensional lattice [Formula: see text] , where [Formula: see text] is the discrete Laplacian and [Formula: see text] is of rank-one. We prove that there exist coupling constant thresholds [Formula: see text] such that for any [Formula: see text] the discrete spectrum of [Formula: see text] is empty and for any [Formula: see text] the discrete spectrum of [Formula: see text] is a singleton [Formula: see text] and [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text] Moreover, we study the asymptotics of [Formula: see text] as [Formula: see text] and [Formula: see text] as well as [Formula: see text] The asymptotics highly depends on d and [Formula: see text]
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spelling pubmed-89835842022-04-22 Expansion of eigenvalues of the perturbed discrete bilaplacian Kholmatov, Shokhrukh Yu. Khalkhuzhaev, Ahmad Pardabaev, Mardon Mon Hefte Math Article We consider the family [Formula: see text] of discrete Schrödinger-type operators in d-dimensional lattice [Formula: see text] , where [Formula: see text] is the discrete Laplacian and [Formula: see text] is of rank-one. We prove that there exist coupling constant thresholds [Formula: see text] such that for any [Formula: see text] the discrete spectrum of [Formula: see text] is empty and for any [Formula: see text] the discrete spectrum of [Formula: see text] is a singleton [Formula: see text] and [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text] Moreover, we study the asymptotics of [Formula: see text] as [Formula: see text] and [Formula: see text] as well as [Formula: see text] The asymptotics highly depends on d and [Formula: see text] Springer Vienna 2022-02-05 2022 /pmc/articles/PMC8983584/ /pubmed/35464818 http://dx.doi.org/10.1007/s00605-022-01678-1 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Kholmatov, Shokhrukh Yu.
Khalkhuzhaev, Ahmad
Pardabaev, Mardon
Expansion of eigenvalues of the perturbed discrete bilaplacian
title Expansion of eigenvalues of the perturbed discrete bilaplacian
title_full Expansion of eigenvalues of the perturbed discrete bilaplacian
title_fullStr Expansion of eigenvalues of the perturbed discrete bilaplacian
title_full_unstemmed Expansion of eigenvalues of the perturbed discrete bilaplacian
title_short Expansion of eigenvalues of the perturbed discrete bilaplacian
title_sort expansion of eigenvalues of the perturbed discrete bilaplacian
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8983584/
https://www.ncbi.nlm.nih.gov/pubmed/35464818
http://dx.doi.org/10.1007/s00605-022-01678-1
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