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We consider a class of self-adjoint Sturm-Liouville problems with rational functions of the spectral parameter in the boundary conditions. The uniform stability for direct and inverse spectral problems is proved for the first time for…

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

This paper presents a new approach to the two-interval Sturm-Liouville eigenfunction expansions, based essentially on the method of integral equations. We consider the Sturm-Liouville problem together with two supplementary transmission…

Classical Analysis and ODEs · Mathematics 2013-12-12 K. Aydemir , O. Sh. Mukhtarov

In this paper we consider the Sturm-Liouville equation -y"+qy = lambda*y on the half line (0,infinity) under the assumptions that x=0 is a regular singular point and nonoscillatory for all real lambda, and that either (i) q is L_1 near…

Numerical Analysis · Mathematics 2013-03-13 Charles Fulton , David Pearson , Steven Pruess

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with…

Spectral Theory · Mathematics 2016-02-23 Natalia Bondarenko

Given a finite set of eigenvalues of a regular Sturm-Liouville problem for the equation -y{\prime}{\prime}+q(x)y={\lambda}y, the potential q(x) of which is unknown. We show the possibility to compute more eigenvalues without any additional…

Classical Analysis and ODEs · Mathematics 2024-10-23 Vladislav V. Kravchenko

We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…

Spectral Theory · Mathematics 2020-10-28 S. A. Buterin , M. A. Malyugina , C. -T. Shieh

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

We prove some new results which justify the use of interval truncation as a means of regularising a singular fourth order Sturm-Liouville problem near a singular endpoint. Of particular interest are the results in the so called lim-3 case,…

Spectral Theory · Mathematics 2007-05-23 Malcolm Brown , Leon Greenberg , Marco Marletta

Spectral problems are considered generated by the Sturm-Liouville equation on connected simple equilateral graphs with the Neumann and Dirichlet boundary conditions at the pendant vertices and continuity and Kirchhoff's conditions at the…

Mathematical Physics · Physics 2022-03-24 Anastasia Chernyshenko , Vyacheslav Pivovarchik

We establish various uniqueness results for inverse spectral problems of Sturm-Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the case of…

Spectral Theory · Mathematics 2012-10-04 Mohammad Shahriari , Aliasghar Jodayree Akbarfam , Gerald Teschl

In this paper, by using the similar methods of [O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694] we extend some…

Classical Analysis and ODEs · Mathematics 2013-04-23 Erdoğan Şen

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

In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace…

Mathematical Physics · Physics 2007-05-23 Christophe Sabot

A new method for solving inverse spectral problems on quantum star graphs is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The representations admit estimates…

Classical Analysis and ODEs · Mathematics 2024-10-23 Sergei A. Avdonin , Vladislav V. Kravchenko

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

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 paper deals with the Neumann spectral problem for a singularly perturbed second order elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue…

Analysis of PDEs · Mathematics 2015-03-24 A. Piatnitski , A. Rybalko , V. Rybalko

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

The purpose of this paper is to investigate some spectral properties of Sturm-Liouville type problems with interior singularities. Some of the mathematical aspects necessary for developing own technique presented. By applying this technique…

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

The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…

Numerical Analysis · Mathematics 2018-03-08 Po-Yi Wu , Cheng-Hong Robert Kao , Tony Wen-Hann Sheu