scholarly journals An inverse spectral problem for non-selfadjoint Sturm-Liouville operators with nonseparated boundary conditions

2012 ◽  
Vol 43 (2) ◽  
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Inverse Spectral Problem ◽  
Nonseparated Boundary Conditions ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Liouville Operators

scholarly journals An inverse spectral problem for non-selfadjoint Sturm-Liouville operators with nonseparated boundary conditions

2012 ◽  
Vol 43 (2) ◽  
pp. 289-299 ◽  
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Inverse Spectral Problem ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Nonseparated Boundary Conditions ◽  
Sturm Liouville ◽  
Liouville Operators

Non-selfadjoint Sturm-Liouville operators on a finite interval with nonseparated boundary conditions are studied. We establish properties of the spectral characteristics and investigate an inverse problem of recovering the operators from their spectral data. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing the solution.

scholarly journals Inverse spectral boundary problem Sturm Liouville type with constant delay and non-zero initial function

2021 ◽  
Vol 51 ◽  
pp. 18-30
Author(s):  
Milenko Pikula ◽  
Dragana Nedić ◽  
Ismet Kalco ◽  
Ljiljanka Kvesić
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Boundary Problem ◽  
Initial Function ◽  
Inverse Spectral Problem ◽  
Constant Delay ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
The Right

This paper is dedicated to solving of the direct and inverse spectral problem for Sturm Liouville type of operator with constant delay from 𝜋/2 to 𝜋, non-zero initial function and Robin’s boundary conditions. It has been proved that two series of eigenvalues unambiguously define the following parameters: delay, coefficients of delay within boundary conditions, the potential on the segment from the point of delay to the right-hand side of the distance and the product of the starting function and potential from the left end of the distance to the delay point.

scholarly journals An inverse spectral problem for Sturm-Liouville operators with singular potentials on arbitrary compact graphs

2019 ◽  
Vol 50 (3) ◽  
pp. 293-305
Author(s):  
S. V. Vasiliev
Keyword(s):  
Inverse Problems ◽  
Spectral Problem ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Singular Potentials ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Weyl Functions ◽  
Liouville Operators

Sturm-Liouville differential operators with singular potentials on arbitrary com- pact graphs are studied. The uniqueness of recovering operators from Weyl functions is proved and a constructive procedure for the solution of this class of inverse problems is provided.

scholarly journals Solution of a model inverse spectral problem for the Sturm-Liouville operator on a graph

2016 ◽  
pp. 204-211
Author(s):  
Н.Ф. Валеев ◽  
Ю.В. Мартынова ◽  
Я.Т. Султанаев
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Dimensional Space ◽  
Geometric Graph ◽  
Finite Dimensional Space ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Model Inverse

Исследуется модельная обратная спектральная задача для оператора Штурма-Лиувилля на геометрическом графе. Суть данной задачи состоит в восстановлении $N$ параметров граничных условий по $N$ собственным значениям. Установлено, что эта задача обладает свойством монотонной зависимости собственных значений от параметров граничных условий. Поставленная задача сведена к многопараметрической обратной спектральной задаче для оператора в конечномерном пространстве. Предложен новый алгоритм численного решения рассматриваемой задачи. A model inverse spectral problem for the Sturm-Liouville operator on a geometric graph is studied. This problem consists in finding $N$ parameters of the boundary conditions using its $N$ known eigenvalues. It is shown that the problem under consideration possess the property of a monotonic dependence of its eigenvalues on the parameters of the boundary conditions. This problem is reduced to a multiparameter inverse spectral problem for the operator in a finite-dimensional space. A new algorithm for the numerical solution of this problem is proposed.

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