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The inverse problem of determining the order of the fractional Riemann- Liouville derivative with respect to time in the subdi_usion equation with an arbitrary positive self-adjoint operator having a discrete spectrum is considered. Using…

General Mathematics · Mathematics 2021-08-12 Shavkat Alimov , Ravshan Ashurov

Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…

Spectral Theory · Mathematics 2013-02-19 Emrah Yilmaz , Hikmet Kemaloglu

We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…

Mathematical Physics · Physics 2018-11-15 William Rundell , Masahiro Yamamoto

We give a brief overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS) and propose a new method for numerical solution of corresponding…

Classical Analysis and ODEs · Mathematics 2012-11-08 Vladislav V. Kravchenko , Sergii M. Torba

This is a correction to our article in the Journal of Differential Equations, Volume 76(1988).

Spectral Theory · Mathematics 2010-07-06 Jean-Claude Guillot , James V. Ralston

The paper deals with Sturm-Liouville-type operators with frozen argument of the form $\ell y:=-y''(x)+q(x)y(a),$ $y^{(\alpha)}(0)=y^{(\beta)}(1)=0,$ where $\alpha,\beta\in\{0,1\}$ and $a\in[0,1]$ is an arbitrary fixed rational number. Such…

Spectral Theory · Mathematics 2023-07-19 Tzong-Mo Tsai , Hsiao-Fan Liu , Sergey Buterin , Lung-Hui Chen , Chung-Tsun Shieh

The notion of the wave spectrum of a semi-bounded symmetric operator was introduced by one of the authors in 2013. The wave spectrum is a topological space determined by the operator in a canonical way. The definition uses a dynamical…

Spectral Theory · Mathematics 2017-03-02 M. I. Belishev , S. A. Simonov

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 study spectral problems for the Sturm-Liouville operator with arbitrary complexvalued potential q(x) and two-point boundary conditions. All types of mentioned boundary conditions are considered. We ivestigate in detail the…

Spectral Theory · Mathematics 2015-12-22 Alexander Makin

Consider the operator $H\p=-\p''+q\p=\l\p$, $\p(0)=0$, $\p'(1)+b\p(1)=0$ acting in $L^2(0,1)$, where $q\in L^2(0,1)$ is a real potential. Let $\l_n(q,b)$, $n\ge 0$, be the eigenvalues of $H$ and $\n_n(q,b)$ be the so-called norming…

Spectral Theory · Mathematics 2007-05-23 Dmitri Chelkak , Evgeny Korotyaev

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

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

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

Spectral problem for a family of periodic Sturm--Liouville problems \[ u''+\lambda^2(a(x)-a)u=0 \] depending on the parameter (a\in\mathbb R) is considered. An interpolation formula describing the behaviour of the branches of the spectrum…

Spectral Theory · Mathematics 2007-05-23 D. A. Popov

The paper investigates spectral properties of multi-interval Sturm-Liouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions in terms of boundary…

Spectral Theory · Mathematics 2020-04-22 Andrii Goriunov

We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in…

Spectral Theory · Mathematics 2011-01-27 I. Karabash , C. Trunk

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

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 study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists in the complete separability of the Hamilton-Jacobi equations for the…

Mathematical Physics · Physics 2014-09-23 Thierry Daudé , Niky Kamran , François Nicoleau

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth