Abstract
In this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 19-01-00102
Award Identifier / Grant number: 20-31-70005
Funding source: Ministry of Science and Technology, Taiwan
Award Identifier / Grant number: 106-2115-M-032-004
Funding statement: This work was supported by the Mathematics Research Promotion Center of Taiwan. The author N. P. Bondarenko was also supported by Grants 20-31-70005 and 19-01-00102 of the Russian Foundation for Basic Research. The author Chung-Tsun Shieh was partially supported by Ministry of Science and Technology, Taiwan under Grant 106-2115-M-032-004.
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