On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter

Abstract Inverse nodal problems for Sturm–Liouville equations associated with boundary conditions polynomially dependent on the spectral parameter are studied. The authors show that a twin-dense subset WB([a,b]) $W_{B}([a,b])$ can uniquely determine the operator up to a constant translation of eigen...

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Main Authors:	Yu Ping Wang, Ko Ya Lien, Chung Tsun Shieh
Format:	Article
Language:	English
Published:	SpringerOpen 2018-03-01
Series:	Boundary Value Problems
Subjects:	Inverse spectral problem Inverse nodal problem Spectral parameter Potential Weyl m-function
Online Access:	http://link.springer.com/article/10.1186/s13661-018-0948-4

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spelling	doaj-d19ad53928a74aa0b48af22d6027bbf72020-11-24T22:08:44ZengSpringerOpenBoundary Value Problems1687-27702018-03-012018111110.1186/s13661-018-0948-4On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameterYu Ping Wang0Ko Ya Lien1Chung Tsun Shieh2Department of Applied Mathematics, Nanjing Forestry UniversityDepartment of Mathematics, Tamkang UniversityDepartment of Mathematics, Tamkang UniversityAbstract Inverse nodal problems for Sturm–Liouville equations associated with boundary conditions polynomially dependent on the spectral parameter are studied. The authors show that a twin-dense subset WB([a,b]) $W_{B}([a,b])$ can uniquely determine the operator up to a constant translation of eigenparameter and potential, where [a,b] $[a,b]$ is an arbitrary interval which contains the middle point of the domain of the operator and B is a subset of N $\mathbb {N}$ which satisfies some condition (see Theorem 4.2).http://link.springer.com/article/10.1186/s13661-018-0948-4Inverse spectral problemInverse nodal problemSpectral parameterPotentialWeyl m-function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yu Ping Wang Ko Ya Lien Chung Tsun Shieh
spellingShingle	Yu Ping Wang Ko Ya Lien Chung Tsun Shieh On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter Boundary Value Problems Inverse spectral problem Inverse nodal problem Spectral parameter Potential Weyl m-function
author_facet	Yu Ping Wang Ko Ya Lien Chung Tsun Shieh
author_sort	Yu Ping Wang
title	On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter
title_short	On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter
title_full	On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter
title_fullStr	On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter
title_full_unstemmed	On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter
title_sort	on a uniqueness theorem of sturm–liouville equations with boundary conditions polynomially dependent on the spectral parameter
publisher	SpringerOpen
series	Boundary Value Problems
issn	1687-2770
publishDate	2018-03-01
description	Abstract Inverse nodal problems for Sturm–Liouville equations associated with boundary conditions polynomially dependent on the spectral parameter are studied. The authors show that a twin-dense subset WB([a,b]) $W_{B}([a,b])$ can uniquely determine the operator up to a constant translation of eigenparameter and potential, where [a,b] $[a,b]$ is an arbitrary interval which contains the middle point of the domain of the operator and B is a subset of N $\mathbb {N}$ which satisfies some condition (see Theorem 4.2).
topic	Inverse spectral problem Inverse nodal problem Spectral parameter Potential Weyl m-function
url	http://link.springer.com/article/10.1186/s13661-018-0948-4
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On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter

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