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Inverse nodal problems on quantum tree graphs

Part of: Boundary value problems General theory in ordinary differential equations Operator theory: Ordinary differential operators

Published online by Cambridge University Press:  16 December 2021

Chuan-Fu Yang  and
Dai-Quan Liu
Chuan-Fu Yang
Affiliation:
Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People's Republic of China (chuanfuyang@njust.edu.cn, daiquanliu@njust.edu.cn)
Dai-Quan Liu
Affiliation:
Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People's Republic of China (chuanfuyang@njust.edu.cn, daiquanliu@njust.edu.cn)
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Abstract

We consider inverse nodal problems for the Sturm–Liouville operators on the tree graphs. Can only dense nodes distinguish the tree graphs? In this paper it is shown that the data of dense-nodes uniquely determines the potential (up to a constant) on the tree graphs. This provides interesting results for an open question implied in the paper.

Keywords

Caterpillar graphTree graphSturm–Liouville operatorInverse nodal problem

MSC classification

Primary: 34A55: Inverse problems
Secondary: 34B45: Boundary value problems on graphs and networks 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 1 , February 2023 , pp. 275 - 288
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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