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- Title
On the Uniqueness of the Solution of the Inverse Sturm-Liouville Problem with Nonseparated Boundary Conditions on a Geometric Graph.
- Authors
Sadovnichy, V. A.; Sultanaev, Ya. T.; Akhtyamov, A. M.
- Abstract
For the first time, the inverse Sturm-Liouville problem with nonseparated boundary conditions is studied on a star-shaped geometric graph with three edges. It is shown that the Sturm-Liouville problem with general boundary conditions cannot be uniquely reconstructed from four spectra. Nonseparated boundary conditions are found for which a uniqueness theorem for the solution of the inverse Sturm-Liouville problem is proved. The spectrum of the boundary value problem itself and the spectra of three auxiliary problems are used as reconstruction data. It is also shown that the Sturm-Liouville problem with these nonseparated boundary conditions can be uniquely recovered if three spectra of auxiliary problems are used as reconstruction data and only five of its eigenvalues are used instead of the entire spectrum of the problem.
- Subjects
BOUNDARY value problems; COMPLEX variables; STURM-Liouville equation; NUMERICAL solutions to Sturm-Liouville equations; DIFFERENTIAL equations
- Publication
Doklady Mathematics, 2018, Vol 98, Issue 1, p338
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562418050113