English
Related papers

Related papers: Inverse problems for a conformable fractional Stur…

200 papers

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

In the paper, we study the problem of recovering the potential from the spectrum of the Dirichlet boundary value problem for a Sturm--Liouville equation with frozen argument on a closed set. We consider the case when the closed set consists…

Spectral Theory · Mathematics 2024-04-12 Maria Kuznetsova

We consider an inverse optimization spectral problem for the Sturm-Liouville operator $$\mathcal{L}[q] u:=-u''+q(x)u$$ subject to the separated boundary conditions. In the main result, we prove that this problem is related to the existence…

Analysis of PDEs · Mathematics 2018-09-05 Y. Sh. Ilyasov , N. F. Valeev

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants.…

Spectral Theory · Mathematics 2007-05-23 R. O. Hryniv , Ya. V. Mykytyuk

In this work, a boundary value problem for Sturm-Liouville operator with discontinuous coefficient is examined. The main equation is obtained which has an important role in solution of inverse problem for boundary value problem and…

Classical Analysis and ODEs · Mathematics 2016-10-31 Khanlar R. Mamedov , Done Karahan

In the paper we propose a direct method for recovering the Sturm-Liouville potential from the Weyl-Titchmarsh $m$-function given on a countable set of points. We show that using the Fourier-Legendre series expansion of the transmutation…

Classical Analysis and ODEs · Mathematics 2021-07-07 Vladislav V. Kravchenko , Sergii M. Torba

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

We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko

We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…

Spectral Theory · Mathematics 2015-03-06 Vjacheslav Yurko

In this paper, partial inverse problems for the quadratic pencil of Sturm-Liouville operators on a graph with a loop were studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the…

Spectral Theory · Mathematics 2020-05-12 Natalia P. Bondarenko , Chung-Tsun Shieh

In the paper, we study an inverse spectral problem for quadratic pencils of the Sturm--Liouville operators with singular coefficients and entire functions in the boundary conditions. We prove that a subspectrum is sufficient for recovering…

Spectral Theory · Mathematics 2022-04-26 Maria Kuznetsova

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

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

Classical Analysis and ODEs · Mathematics 2008-04-15 R. F. Efendiev

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

Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm…

Spectral Theory · Mathematics 2019-06-18 Chuan-Fu Yang , Natalia P. Bondarenko

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

We introduce and present the general solution of three two-term fractional differential equations of mixed Caputo/Riemann Liouville type. We then solve a Dirichlet type Sturm-Liouville eigenvalue problem for a fractional differential…

Classical Analysis and ODEs · Mathematics 2017-12-29 Mohammad Dehghan , Angelo B. Mingarelli

In this paper, inverse spectral problems for Sturm-Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b - 1 spectral sets uniquely determine the potential…

Spectral Theory · Mathematics 2016-09-13 Natalia Bondarenko , Chung-Tsun Shieh

In this paper, we explore the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this fixed star-like graph centered at the origin as its vertex, we attach $m$ edges. On each edge, we impose the Sturm-Liouville…

Mathematical Physics · Physics 2025-08-18 Lung-Hui Chen

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