scholarly journals Direct and Inverse Problems for the Matrix Sturm–Liouville Operator with General Self-Adjoint Boundary Conditions

2021 ◽  
Vol 109 (3-4) ◽  
pp. 358-378
Author(s):  
N. P. Bondarenko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Direct And Inverse Problems ◽  
The Matrix ◽  
Sturm Liouville

Partial inverse problems for the Sturm–Liouville operator on a star-shaped graph with mixed boundary conditions

2018 ◽  
Vol 26 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Mixed Boundary ◽  
Constructive Method ◽  
Asymptotic Formulas ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph

AbstractThe Sturm–Liouville operator on a star-shaped graph with different types of boundary conditions (Robin and Dirichlet) in different vertices is studied. Asymptotic formulas for the eigenvalues are derived and partial inverse problems are solved: we show that the potential on one edge can be uniquely determined by different parts of the spectrum if the potentials on the other edges are known. We provide a constructive method for the solution of the inverse problems, based on the Riesz basis property of some systems of vector functions.

scholarly journals Double Discontinuous Inverse Problems for Sturm-Liouville Operator with Parameter-Dependent Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
A. S. Ozkan ◽  
B. Keskin ◽  
Y. Cakmak
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Operator ◽  
Weyl Function ◽  
Spectral Sequences ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Parameter Dependent

The purpose of this paper is to solve the inverse spectral problems for Sturm-Liouville operator with boundary conditions depending on spectral parameter and double discontinuities inside the interval. It is proven that the coefficients of the problem can be uniquely determined by either Weyl function or given two different spectral sequences.

scholarly journals Inverse spectral problem for the matrix Sturm-Liouville operator with the general separated self-adjoint boundary conditions

2019 ◽  
Vol 50 (3) ◽  
pp. 321-336 ◽  
Author(s):  
Xiao-Chuan Xu
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Liouville Operator ◽  
General Type ◽  
Inverse Spectral Problem ◽  
Uniqueness Theorems ◽  
Unitary Matrices ◽  
Weyl Matrix ◽  
The Matrix ◽  
Sturm Liouville

In this work, we study the matrix Sturm-Liouville operator with the separated self-adjoint boundary conditions of general type, in terms of two unitary matrices. Some properties of the eigenvalues and the normalization matrices are given. Uniqueness theorems for determining the potential and the unitary matrices in the boundary conditions from the Weyl matrix, two characteristic matrices or one spectrum and the corresponding normalization matrices are proved.

scholarly journals Direct and Inverse Problems for Sturm-Liouville Operator Which Has Discontinuity Conditions and Coulomb Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yalçın Güldü ◽  
Merve Arslantaş
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Coulomb Potential ◽  
Liouville Operator ◽  
Direct And Inverse Problems ◽  
Main Equation ◽  
Sturm Liouville ◽  
Discontinuity Conditions

We give a derivation of the main equation for Sturm-Liouville operator with Coulomb potential and prove its unique solvability. Using the solution of the main equation, we get an algorithm for the solution of the inverse problem.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

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