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Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction

In the paper, the spectral problem generated by the Sturm-Liouville equation -y'' + q(x)y = (λ² - ip(x)λ)y, where q(x) is a real L₂(0, a)-function and p(x) is a peace-wise constant, is considered with the Dirichlet boundary conditions at the ends of the interval (0, a). The spectrum of the...

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Bibliographic Details
Main Author:	Kobyakova, L.
Format:	Article
Language:	English
Published:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2012
Series:	Журнал математической физики, анализа, геометрии
Online Access:	http://dspace.nbuv.gov.ua/handle/123456789/106724
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id	irk-123456789-106724
record_format	dspace
spelling	irk-123456789-1067242016-10-04T03:02:32Z Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction Kobyakova, L. In the paper, the spectral problem generated by the Sturm-Liouville equation -y'' + q(x)y = (λ² - ip(x)λ)y, where q(x) is a real L₂(0, a)-function and p(x) is a peace-wise constant, is considered with the Dirichlet boundary conditions at the ends of the interval (0, a). The spectrum of the problem is compared with the spectra of auxiliary problems with the Dirichlet-Dirichlet and the Dirichlet-Neumann boundary conditions on the halves of the interval. Asymptotic formulas are obtained for the eigenvalues of this problem. В статье рассматривается спектральная задача, порожденная уравнением Штурма-Лиувилля -y'' + q(x)y = (λ² - ip(x)λ)y, где q(x) - вещественная L₂(0, a)-функция, а p(x) является кусочно-постоянной, с краевыми условиями Дирихле на концах интервала (0, a). Спектр данной задачи сравнивается со спектром вспомогательной задачи с краевыми условиями Дирихле-Дирихле и Дирихле-Неймана на полуинтервалах. Получены асимптотические формулы для собственных значений задачи. 2012 Article Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction / L. Kobyakova // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 3. — С. 280-295. — Бібліогр.: 19 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106724 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, the spectral problem generated by the Sturm-Liouville equation -y'' + q(x)y = (λ² - ip(x)λ)y, where q(x) is a real L₂(0, a)-function and p(x) is a peace-wise constant, is considered with the Dirichlet boundary conditions at the ends of the interval (0, a). The spectrum of the problem is compared with the spectra of auxiliary problems with the Dirichlet-Dirichlet and the Dirichlet-Neumann boundary conditions on the halves of the interval. Asymptotic formulas are obtained for the eigenvalues of this problem.
format	Article
author	Kobyakova, L.
spellingShingle	Kobyakova, L. Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction Журнал математической физики, анализа, геометрии
author_facet	Kobyakova, L.
author_sort	Kobyakova, L.
title	Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction
title_short	Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction
title_full	Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction
title_fullStr	Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction
title_full_unstemmed	Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction
title_sort	spectral problem generated by the equation of smooth string with piece-wise constant friction
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2012
url	http://dspace.nbuv.gov.ua/handle/123456789/106724
citation_txt	Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction / L. Kobyakova // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 3. — С. 280-295. — Бібліогр.: 19 назв. — англ.
series	Журнал математической физики, анализа, геометрии
work_keys_str_mv	AT kobyakoval spectralproblemgeneratedbytheequationofsmoothstringwithpiecewiseconstantfriction
first_indexed	2023-10-18T20:13:33Z
last_indexed	2023-10-18T20:13:33Z
_version_	1796149302663315456

Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction

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