On the Uniqueness of the Solution of the Inverse Sturm-Liouville Problem with Nonseparated Boundary Conditions on a Geometric Graph

For the first time, the inverse Sturm-Liouville problem with nonseparated boundary conditions is studied on a star-shaped geometric graph of three edges. It is shown that the Sturm-Liouville problem with common boundary conditions can not be restored uniquely by four spectra. Nonseparated boundary conditions are found for which the uniqueness theorem for the solution of the inverse Sturm-Liouville problem is proved. As the reconstruction data, the spectrum of the boundary value problem itself and the spectra of three auxiliary problems were used. It is also shown that the Sturm-Liouville problem with these nonseparated boundary conditions can be restored uniquely if three auxiliary problems are used as recovery data, and only five of its eigenvalues are used instead of the spectrum of the problem itself.

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14.10.2018

Publication date

16.10.2018

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808

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GOST	Sadovnichy V., Sultanaev Y., Akhtyamov A. On the Uniqueness of the Solution of the Inverse Sturm-Liouville Problem with Nonseparated Boundary Conditions on a Geometric Graph // Doklady Akademii nauk – 2018. – V. 481. – Issue 3 C. 247-249 [Electronic resource]. URL: http://ras.jes.su/dan/s207987840000610-0-1-en (circulation date: 03.05.2024). DOI: 10.31857/S086956520001371-1
MLA	Sadovnichy, Victor, Sultanaev, Ya, Akhtyamov, A. "On the Uniqueness of the Solution of the Inverse Sturm-Liouville Problem with Nonseparated Boundary Conditions on a Geometric Graph." Doklady Akademii nauk 481.3 (2018):247-249. DOI: 10.31857/S086956520001371-1
APA	Sadovnichy V., Sultanaev Y., Akhtyamov A. (2018). On the Uniqueness of the Solution of the Inverse Sturm-Liouville Problem with Nonseparated Boundary Conditions on a Geometric Graph. Doklady Akademii nauk 481(3), pp.247-249 DOI: 10.31857/S086956520001371-1

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