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Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument

Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument

In the paper, we are concerned with spectral properties of discontinuous Sturm–Liouville type problems with retarded argument. We extend and generalize some approaches and results of the classical regular and discontinuous Sturm–Liouville problems. First, we study the spectral properties of a Sturm–...

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Main Author: Erdoğan Şen
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2018
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/145860
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spelling irk-123456789-1458602019-02-02T01:23:12Z Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument Erdoğan Şen In the paper, we are concerned with spectral properties of discontinuous Sturm–Liouville type problems with retarded argument. We extend and generalize some approaches and results of the classical regular and discontinuous Sturm–Liouville problems. First, we study the spectral properties of a Sturm–Liouville problem on the half-axis and obtain lower bounds for the eigenvalues of this problem. Then we study spectral properties of a Sturm–Liouville problem with discontinuous weight function which contains a spectral parameter in the boundary conditions. We also obtain asymptotic formulas for eigenvalues and eigenfunctions of this problem and bounds for the distance between eigenvalues. У данiй статтi ми маємо справу iз спектральними властивостями розривних задач типу Штурма Лiувiлля iз запiзненням аргументу. Ми розширюємо i узагальнюємо деякi пiдходи i результати класичних регулярних i розривних задач Штурма Лiувiлля. Спочатку ми вивчаємо спектральнi властивостi задачi Штурма Лiувiлля на пiвосi й отримуємо нижнi оцiнки для власних значень задачi. Потiм ми вивчаємо спектральнi властивостi задачi Штурма Лiувiлля з розривною ваговою функцiєю, яка мiстить спектральний параметр в крайових умовах. Ми також отримуємо асимптотичнi формули для власних значень i власних функцiй задачi та межi вiдстанi мiж власними значеннями. 2018 Article Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument / Erdoğan Şen // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 78-99. — Бібліогр.: 24 назв. — англ. 1812-9471 DOI: https://doi.org/10.15407/mag14.01.078 Mathematics Subject Classification 2010: 34L15, 34L20, 35R10 http://dspace.nbuv.gov.ua/handle/123456789/145860 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description In the paper, we are concerned with spectral properties of discontinuous Sturm–Liouville type problems with retarded argument. We extend and generalize some approaches and results of the classical regular and discontinuous Sturm–Liouville problems. First, we study the spectral properties of a Sturm–Liouville problem on the half-axis and obtain lower bounds for the eigenvalues of this problem. Then we study spectral properties of a Sturm–Liouville problem with discontinuous weight function which contains a spectral parameter in the boundary conditions. We also obtain asymptotic formulas for eigenvalues and eigenfunctions of this problem and bounds for the distance between eigenvalues.
format Article
author Erdoğan Şen
spellingShingle Erdoğan Şen
Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument
Журнал математической физики, анализа, геометрии
author_facet Erdoğan Şen
author_sort Erdoğan Şen
title Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument
title_short Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument
title_full Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument
title_fullStr Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument
title_full_unstemmed Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument
title_sort spectral analysis of discontinuous boundary-value problems with retarded argument
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2018
url http://dspace.nbuv.gov.ua/handle/123456789/145860
citation_txt Spectral Analysis of Discontinuous Boundary-Value Problems with Retarded Argument / Erdoğan Şen // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 78-99. — Бібліогр.: 24 назв. — англ.
series Журнал математической физики, анализа, геометрии
work_keys_str_mv AT erdogansen spectralanalysisofdiscontinuousboundaryvalueproblemswithretardedargument
first_indexed 2023-05-20T17:23:16Z
last_indexed 2023-05-20T17:23:16Z
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