English
Related papers

Related papers: Inverse nodal problems for Sturm-Liouville equatio…

200 papers

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 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

This paper develops a methodological framework for addressing a novel and application-oriented inverse nodal problem in Sturm-Liouville operators, having significant applications in seismic wave analysis and submarine underwater radar…

Classical Analysis and ODEs · Mathematics 2025-06-27 Yuchao He , Mengda Wu , Yonghui Xia , Meirong Zhang

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient conditions under which the root vectors of this Sturm-Liouville problem can be…

Classical Analysis and ODEs · Mathematics 2012-06-11 Paul Binding , Branko Ćurgus

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

This paper explores the complexity associated with solving the inverse Sturm-Liouville problem with Robin boundary conditions: given a sequence of eigenvalues and a sequence of norming constants, how many limits does a universal algorithm…

Numerical Analysis · Mathematics 2023-12-27 Jonathan Ben-Artzi , Marco Marletta , Frank Rösler

We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…

Spectral Theory · Mathematics 2021-07-13 S. A. Buterin , M. A. Kuznetsova , V. A. Yurko

In this work, we use the \textit{regularized sampling method} to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their…

Spectral Theory · Mathematics 2007-05-23 Bilal Chanane

Inverse problems for differential pencils with nonlocal conditions are investigated. Several uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl…

Spectral Theory · Mathematics 2015-03-09 Chuan-Fu Yang , Vjacheslav Yurko

We study characteristic functions and describe asymptotics of the eigenvalues for the spectral Sturm-Liouville problem on graphs equipped with Robin-Kirhhoff boundary conditions. Also, we show how to recover the coefficients in the Robin…

Spectral Theory · Mathematics 2026-02-17 Yuri Latushkin , Vyacheslav Pivovarchik , Alesia Supranovych

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

In this paper, we investigate the sampling analysis associated with discontinuous Sturm-Liouville problem which has transmission conditions at two points of discontinuity also contains an eigenparameter in a boundary condition and two…

Classical Analysis and ODEs · Mathematics 2015-02-27 Fatma Hira , Nihat Altinisik

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

Necessary and sufficient conditions for two sequences $\{\mu_n\}_{n=0}^\infty$ and $\{ a_n\}_{n=0}^\infty$ to be the spectral data for a certain Sturm-Liouville problem are well known. We add two more conditions so that the same two…

Spectral Theory · Mathematics 2016-08-17 Tigran Harutyunyan , Yuri Ashrafyan

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

In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their…

Spectral Theory · Mathematics 2020-08-10 Maria Kuznetsova

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter. We give sufficient conditions under which a basis of each root subspace for this…

Classical Analysis and ODEs · Mathematics 2012-06-11 Paul Binding , Branko Ćurgus

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 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

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