The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph

Xian-Biao Wei (), Yan-Hsiou Cheng and Yu-Ping Wang
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Xian-Biao Wei: Department of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Yan-Hsiou Cheng: Department of Mathematics and Information Education, National Taipei University of Education, Taipei City 106, Taiwan
Yu-Ping Wang: Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China

Mathematics, 2022, vol. 10, issue 21, 1-21

Abstract: We firstly prove the Horváth-type theorem for Sturm–Liouville operators on a star-shaped graph and then solve a new partial inverse nodal problem for this operator. We give some algorithms to recover this operator from a dense nodal subset and prove uniqueness theorems from paired-dense nodal subsets in interior subintervals having a central vertex. In particular, we obtain some uniqueness theorems by replacing the information of nodal data on some fixed edge with part of the eigenvalues under some conditions.

Keywords: partial inverse spectral problem; partial inverse nodal problem; boundary value problem; graph; paired-dense nodal subset (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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