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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 the present paper, motivated by point interaction, we propose a new and explicit approach to inverse Sturm-Liouville eigenvalue problems under Dirichlet boundary. More precisely, when a given Sturm-Liouville eigenvalue problem with the…

Spectral Theory · Mathematics 2024-07-25 Min Zhao , Jiangang Qi , Xiao Chen

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

In this work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities but also, eigenparameter-dependent boundary conditions and…

Classical Analysis and ODEs · Mathematics 2013-07-02 Serkan Araci , Mehmet Acikgoz , Azad Bayramov , Erdoğan Şen

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

In this paper, we study the inverse spectral problem for the Sturm-Liouville operators on a star-shaped graph, which consists in the recovery of the potentials from specral data or several spectra. The uniform stability of these inverse…

Spectral Theory · Mathematics 2026-01-16 E. E. Chitorkin , N. P. Bondarenko

In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm-Liouville problem that consists in the recovery of the potential and the parameters of…

Spectral Theory · Mathematics 2024-09-25 Natalia P. Bondarenko

This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…

Analysis of PDEs · Mathematics 2026-03-24 Yan Jiang , Hongyu Liu , Kai Zhang , Haoran Zheng

We describe the asymptotic distribution of the eigenvalues of interior transmission problem in absorbing medium. We apply the Cartwright's theory and the technique from asymptotic periodic entire function theory. We find a Weyl's type of…

Functional Analysis · Mathematics 2013-07-02 Lung-Hui Chen

In this study by applying an own technique we investigate some asymptotic approximation properties of new type discontinuous boundary-value problems, which consists of a Sturm-Liouville equation together with eigenparameter-dependent…

Classical Analysis and ODEs · Mathematics 2013-03-29 O. Sh. Mukhtarov , K. Aydemir

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 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

We discuss direct and inverse spectral theory of self-adjoint Sturm-Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl-Titchmarsh theory for these relations.…

Spectral Theory · Mathematics 2012-05-28 Jonathan Eckhardt

The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…

Spectral Theory · Mathematics 2017-07-05 Sonja Currie , Marlena Nowaczyk , Bruce Alastair Watson

In this study, the inverse problem of the scattering theory on the half line for a piecewise continuous Sturm-Liouville equation with boundary condition depending quadratic on the spectral parameter is considered. The scattering data of the…

Spectral Theory · Mathematics 2015-02-06 Kh. R. Mamedov , Nida P. Kosar , F. Ayca Cetinkaya

In this paper, the inverse Sturm-Liouville problem with distribution potential and with polynomials of the spectral parameter in one of the boundary conditions is considered. We for the first time prove local solvability and stability of…

Spectral Theory · Mathematics 2024-02-12 Egor E. Chitorkin , Natalia P. Bondarennko

In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse…

Numerical Analysis · Mathematics 2024-04-25 Nikolaos Pallikarakis , Andreas Ntargaras

We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \begin{equation*} Ly=\frac{1}{r}\left( -(p\left[ y^{\prime }+sy\right] )^{\prime }+sp\left[ y^{\prime…

Spectral Theory · Mathematics 2017-11-21 Jun Yan , Guoliang Shi , Jia Zhao

In the present review we deal with the recently introduced method of spectral parameter power series (SPPS) and show how its application leads to an explicit form of the characteristic equation for different eigenvalue problems involving…

Mathematical Physics · Physics 2012-04-20 K. V. Khmelnytskaya , V. V. Kravchenko , H. C. Rosu

In this paper, we present a new discontinuous Sturm Liouville problem with symmetrically located discontinuities which are defined depending on a neighborhood of a midpoint of the interval. Also the problem contains an eigenparameter in one…

Classical Analysis and ODEs · Mathematics 2015-12-18 Fatma Hira , Nihat Altinisik