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Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…

Spectral Theory · Mathematics 2015-02-02 Vjacheslav Yurko

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

The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the…

Spectral Theory · Mathematics 2014-12-19 Natalia Bondarenko

We consider two main inverse Sturm-Liouville problems: the problem of recovery of the potential and the boundary conditions from two spectra or from a spectral density function. A simple method for practical solution of such problems is…

Numerical Analysis · Mathematics 2021-02-03 Vladislav V. Kravchenko , Sergii M. Torba

This paper is devoted to the study of a partial inverse spectral problem for Sturm-Liouville operators with frozen arguments on a star-shaped graph. The potentials are assumed to be known a priori on all edges except one, and the objective…

Spectral Theory · Mathematics 2025-06-26 Chung-Tsun Shieh , Tzong-Mo Tsai , Meng-Nien Wu

In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…

Spectral Theory · Mathematics 2023-05-31 Feng Wang , Chuan-Fu Yang

Half-inverse spectral problem for a Sturm--Liouville operator consists in reconstruction of this operator by its spectrum and half of the potential. We give the necessary and sufficient conditions for solvability of the half-inverse…

Spectral Theory · Mathematics 2007-05-23 Rostyslav O. Hryniv , Yaroslav V. Mykytyuk

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

The matrix Sturm-Liouville operator on a finite interval with singular potential of class $W_2^{-1}$ and the general self-adjoint boundary conditions is studied. This operator generalizes the Sturm-Liouville operators on geometrical graphs.…

Spectral Theory · Mathematics 2020-07-16 Natalia P. Bondarenko

The paper deals with two inverse problems for Sturm--Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$. The first one is the problem of recovering of a potential by two spectra. We associate with this problem the map $F:\,…

Spectral Theory · Mathematics 2010-10-29 A. M. Savchuk , A. A. Shkalikov

We study the inverse Sturm-Liouville problem on a finite interval from partial knowledge of spectral data. Specifically, we show that the potential can be uniquely reconstructed from the knowledge of a fraction of Dirichlet eigenvalues…

Analysis of PDEs · Mathematics 2026-03-30 Ali Feizmohammadi , Yavar Kian

We consider the spectral problems for the Sturm-Liouville operator generated by the Dirichlet, Neumann, Dirichlet-Neumann and Neumann-Dirichlet conditions. The necessary and sufficient condition for the coincidence of the spectrum of the…

Functional Analysis · Mathematics 2019-12-30 B. N. Biyarov

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

In this work, we study the inverse spectral problems for the Sturm-Liouville operators on [0,1] with complex coefficients and a discontinuity at $x=a\in(0,1)$. Assume that the potential on (a,1) and some parameters in the discontinuity and…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Chuan-Fu Yang , Natalia Pavlovna Bondarenko

We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…

Spectral Theory · Mathematics 2022-06-28 Sergey Buterin , Nebojša Djurić

In this work, we consider the Sturm-Liouville operator on a finite interval $[0,1]$ with discontinuous conditions at $1/2$. We prove that if the potential is known a priori on a subinterval $[b,1]$ with $b\ge1/2$, then parts of two spectra…

Spectral Theory · Mathematics 2017-03-07 Xiao-Chuan Xu , Chuan-Fu Yang

We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…

Spectral Theory · Mathematics 2017-11-16 Natalia P. Bondarenko

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

In this work, a boundary value problem for Sturm-Liouville operator with discontinuous coefficient is examined. The main equation is obtained which has an important role in solution of inverse problem for boundary value problem and…

Classical Analysis and ODEs · Mathematics 2016-10-31 Khanlar R. Mamedov , Done Karahan

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