Inverse Sturm–Liouville Problem with Spectral Parameter in the Boundary Conditions

Natalia P. Bondarenko () and Egor E. Chitorkin
Additional contact information
Natalia P. Bondarenko: Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, 443086 Samara, Russia
Egor E. Chitorkin: Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, 410012 Saratov, Russia

Mathematics, 2023, vol. 11, issue 5, 1-19

Abstract: In this paper, for the first time, we study the inverse Sturm–Liouville problem with polynomials of the spectral parameter in the first boundary condition and with entire analytic functions in the second one. For the investigation of this new inverse problem, we develop an approach based on the construction of a special vector functional sequence in a suitable Hilbert space. The uniqueness of recovering the potential and the polynomials of the boundary condition from a part of the spectrum is proved. Furthermore, our main results are applied to the Hochstadt–Lieberman-type problems with polynomial dependence on the spectral parameter not only in the boundary conditions but also in discontinuity (transmission) conditions inside the interval. We prove novel uniqueness theorems, which generalize and improve the previous results in this direction. Note that all the spectral problems in this paper are investigated in the general non-self-adjoint form, and our method does not require the simplicity of the spectrum. Moreover, our method is constructive and can be developed in the future for numerical solution and for the study of solvability and stability of inverse spectral problems.

Keywords: inverse spectral problems; Sturm–Liouville operator; polynomials in the boundary conditions; entire functions in the boundary conditions; uniqueness theorems; half-inverse problems; discontinuity inside the interval (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/5/1138/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/5/1138/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:5:p:1138-:d:1079640

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().