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

Spectral Theory · Mathematics 2021-04-28 Natalia P. Bondarenko

In this paper, the Sturm-Liouville operators on a graph with a cycle are considered. We study the inverse spectral problem, which consists in the recovery of the potentials from several spectra and a sequence of signs related to the…

Spectral Theory · Mathematics 2025-09-03 Natalia P. Bondarenko

The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…

Spectral Theory · Mathematics 2008-04-08 R. F. Efendiev

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

In this paper, we further Meirong Zhang, et al.'s work by computing the number of weighted eigenvalues for Sturm-Liouville equations, equipped with general integrable potentials and Dirac weights, under Dirichlet boundary condition. We show…

Classical Analysis and ODEs · Mathematics 2021-09-01 Xiao Chen , Jiangang Qi

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…

Spectral Theory · Mathematics 2014-07-15 Natalia 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

The paper is denoted to the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with irregular (distributive) potentials. To obtain a solution to the equation, the separation method and asymptotics of the…

Analysis of PDEs · Mathematics 2022-09-20 Michael Ruzhansky , Serikbol Shaimardan , Alibek Yeskermessuly

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

The purpose of this paper is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with…

Classical Analysis and ODEs · Mathematics 2013-03-28 O. Sh. Mukhtarov , K. Aydemir

In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order ($n > 3$) differential operators with distribution coefficients. The inverse problem consists in the recovery of…

Spectral Theory · Mathematics 2023-09-11 Natalia P. Bondarenko

This paper deals with the computation of the eigenvalues of non self-adjoint Sturm-Liouville problems with parameter dependent boundary conditions using the \textit{regularized sampling method}. A few numerical examples among which singular…

Spectral Theory · Mathematics 2007-05-23 Bilal Chanane

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

We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…

Spectral Theory · Mathematics 2018-04-20 Sonja Currie , Marlena Nowaczyk , Bruce A. Watson

This paper starts a series devoted to the vector-valued Sturm-Liouville problem $-\psi''+V(x)\psi=\lambda\psi$, $\psi\in L^2([0,1];\mathbb{C}^N)$, with separated boundary conditions. The overall goal of the series is to give a complete…

Spectral Theory · Mathematics 2013-12-13 Dmitry Chelkak , Sergey Matveenko

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 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

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 suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, being measured in the direction to a specific boundary…

Spectral Theory · Mathematics 2023-04-28 Sergey Buterin

In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas…

Classical Analysis and ODEs · Mathematics 2015-06-03 Erdoğan Şen , Azad Bayramov