An inverse three spectra problem for Sturm–Liouville operators

In this paper, we consider the inverse three spectra problems of recovering the Sturm–Liouville equation by the spectra of the Neumann–Dirichlet boundary value problem on [ 0 , 1 ] , the Neumann–Robin problem on [ 0 , 1 / 2 ] , and the Robin–Dirichlet problem on [ 1 / 2 , 1 ] , where the two Robin p...

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Bibliographic Details
Published in:Boundary value problems 2018-05, Vol.2018 (1), p.1-14, Article 68
Main Authors: Guo, Yongxia, Wei, Guangsheng, Yao, Ruoxia
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Boundary condition
Boundary value problems
Difference and Functional Equations
Dirichlet problem
Inverse three spectra problem
Liouville equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Spectra
Sturm–Liouville problem
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Summary:In this paper, we consider the inverse three spectra problems of recovering the Sturm–Liouville equation by the spectra of the Neumann–Dirichlet boundary value problem on [ 0 , 1 ] , the Neumann–Robin problem on [ 0 , 1 / 2 ] , and the Robin–Dirichlet problem on [ 1 / 2 , 1 ] , where the two Robin parameters at the interior node x = 1 / 2 are considered to be different. The algorithm of construction is presented and sufficient conditions for three sequences to be the spectral data of the mentioned boundary problems are given.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-018-0987-x