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In this paper, inverse spectral problems for Sturm-Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b - 1 spectral sets uniquely determine the potential…

Spectral Theory · Mathematics 2016-09-13 Natalia Bondarenko , Chung-Tsun Shieh

We suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…

Spectral Theory · Mathematics 2023-04-13 Sergey Buterin , Sergey Vasilev

In the paper, we study an inverse spectral problem for quadratic pencils of the Sturm--Liouville operators with singular coefficients and entire functions in the boundary conditions. We prove that a subspectrum is sufficient for recovering…

Spectral Theory · Mathematics 2022-04-26 Maria Kuznetsova

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…

Classical Analysis and ODEs · Mathematics 2022-03-23 A. Sinan Ozkan , İbrahim Adalar

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

Spectral Theory · Mathematics 2024-09-05 E. E. Chitorkin , N. P. Bondarenko

The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…

Spectral Theory · Mathematics 2011-11-15 Natalia Bondarenko

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and…

Spectral Theory · Mathematics 2015-05-13 Ya. V. Mykytyuk , N. S. Trush

The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the…

Spectral Theory · Mathematics 2017-01-03 Natalia Bondarenko

We prove that the potential of a Sturm--Liouville operator depends analytically and Lipschitz continuously on the spectral data (two spectra or one spectrum and the corresponding norming constants). We treat the class of operators with…

Spectral Theory · Mathematics 2011-01-31 Rostyslav O. Hryniv

Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the…

Spectral Theory · Mathematics 2017-02-28 Natalia P. Bondarenko

In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of…

Spectral Theory · Mathematics 2023-09-11 Egor E. Chitorkin , Natalia P. Bondarenko

We consider Sturm-Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in…

Spectral Theory · Mathematics 2019-04-24 Chuan-Fu Yang , Natalia Bondarenko

This paper deals with the Sturm-Liouville operators with distribution potentials of the space $W_2^{-1}$ on a metric tree. We study an inverse spectral problem that consists in the recovery of the potentials from the characteristic…

Spectral Theory · Mathematics 2025-10-03 Natalia P. Bondarenko

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete…

Spectral Theory · Mathematics 2015-06-04 Rostyslav Hryniv , Nataliya Pronska

This research was devoted to investigate the inverse spectral problem of Sturm-Liouville operator with many frozen arguments. Under some assumptions, the authors obtained uniqueness theorems. At the end, a numerical simulation for the…

Spectral Theory · Mathematics 2024-07-23 Chung-Tsun Shieh , Tzong-Mo Tsai

In the paper, we study the problem of recovering the potential from the spectrum of the Dirichlet boundary value problem for a Sturm--Liouville equation with frozen argument on a closed set. We consider the case when the closed set consists…

Spectral Theory · Mathematics 2024-04-12 Maria Kuznetsova

The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient…

Spectral Theory · Mathematics 2020-09-08 Natalia P. Bondarenko

Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko , Chuan-Fu Yang

A variety of inverse Sturm-Liouville problems is considered, including the two-spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases the…

Classical Analysis and ODEs · Mathematics 2025-06-03 Vladislav V. Kravchenko

We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local…

Spectral Theory · Mathematics 2020-02-13 Natalia P. Bondarenko