Local solvability and stability of inverse problems for Sturm-Liouville operators with a discontinuity

Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm for solving the inverse problems. The key role in our metho...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 268; no. 10; pp. 6173 - 6188
Main Authors Yang, Chuan-Fu, Bondarenko, Natalia P.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.05.2020
Subjects
Constructive solution
Discontinuity condition
Inverse spectral problem
Local solvability
Stability
Sturm-Liouville operator
34L40
34B05
47E05
Inverse spectral problem
Stability
Local solvability
34A55
Sturm-Liouville operator
Discontinuity condition
34B08
Constructive solution
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Summary:Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm for solving the inverse problems. The key role in our method is played by the Riesz-basis property of a special vector-functional system in a Hilbert space. In addition, we obtain a new uniqueness theorem for recovering the potential on a part of the interval, by using a fractional part of the spectrum.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2019.11.035