scholarly journals Reconstruction of the Sturm-Liouville operators on a graph with $\delta'_s$ couplings

2011 ◽  
Vol 42 (3) ◽  
pp. 329-342 ◽  
Author(s):  
ChuanFu Yang
Keyword(s):  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Dense Subset ◽  
Star Graph ◽  
Central Vertex ◽  
Inverse Nodal Problems ◽  
Sturm Liouville ◽  
The Given ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Inverse nodal problems consist in constructing operators from the given zeros of their eigenfunctions. In this work, we deal with the inverse nodal problems of reconstructing the Sturm- Liouville operator on a star graph with $\delta'_s $ couplings at the central vertex. The uniqueness theorem is proved and a constructive procedure for the solution is provided from a dense subset of zeros of the eigenfunctions for the problem as a data.

An inverse problem for Sturm–Liouville operators on the half-line with complex weights

2019 ◽  
Vol 27 (3) ◽  
pp. 439-443
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Half Line ◽  
Sturm Liouville ◽  
The Given ◽  
Complex Valued ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Abstract Second order differential operators on the half-line with complex-valued weights are considered. Properties of spectral characteristics are established, and the inverse problem of recovering operator’s coefficients from the given Weyl-type function is studied. The uniqueness theorem is proved for this class of nonlinear inverse problems, and a number of examples are provided.

Inverse nodal problems for the Sturm–Liouville operator with nonlocal integral conditions

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Yi-Teng Hu ◽  
Chuan-Fu Yang ◽  
Xiao-Chuan Xu
Keyword(s):  
Potential Function ◽  
Liouville Equation ◽  
Liouville Operator ◽  
Dense Subset ◽  
Integral Conditions ◽  
End Points ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Sturm Liouville ◽  
Nonlocal Integral Conditions

AbstractIn this work, we consider inverse nodal problems of the Sturm–Liouville equation with nonlocal integral conditions at two end-points. We prove that a dense subset of nodal points uniquely determine the potential function of the Sturm–Liouville equation up to a constant.

scholarly journals An inverse spectral problem for differential operators with integral delay

2011 ◽  
Vol 42 (3) ◽  
pp. 295-303 ◽  
Author(s):  
Yulia Kuryshova
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Integral Transform ◽  
Main Tool ◽  
One Dimensional ◽  
Sturm Liouville ◽  
The Uniqueness Theorem

The uniqueness theorem is proved for the solution of the inverse spec- tral problem for second-order integro-di®erential operators on a ¯nite interval. These operators are perturbations of the Sturm-Liouville operator with convolution and one- dimensional operators. The main tool is an integral transform connected with solutions of integro-di®erential operators.

Inverse nodal problems for integro-differential operators with a constant delay

2019 ◽  
Vol 27 (4) ◽  
pp. 501-509 ◽  
Author(s):  
Murat Sat ◽  
Chung Tsun Shieh
Keyword(s):  
Integral Operator ◽  
Potential Function ◽  
Liouville Operator ◽  
Differential Operators ◽  
Constant Delay ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Volterra Integral Operator ◽  
Sturm Liouville

Abstract We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.

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 Spectral analysis of singular Sturm-Liouville operators on time scales

2018 ◽  
Vol 72 (1) ◽  
pp. 1 ◽  
Author(s):  
Bilender P. Allahverdiev ◽  
Huseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Time Scales ◽  
Liouville Operator ◽  
Adjoint Operator ◽  
The Self ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper, we consider properties of the spectrum of a Sturm-Liouville<br />operator on time scales. We will prove that the regular symmetric<br />Sturm-Liouville operator is semi-bounded from below. We will also give some<br />conditions for the self-adjoint operator associated with the singular<br />Sturm-Liouville expression to have a discrete spectrum. Finally, we will<br />investigate the continuous spectrum of this operator.

scholarly journals Sturm-Liouville differential operators with deviating argument

2017 ◽  
Vol 48 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Vjacheslav Anatoljevich Yurko ◽  
Sergey Alexandrovich Buterin ◽  
Milenko Pikula
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Second Order ◽  
Constant Delay ◽  
Deviating Argument ◽  
Sturm Liouville ◽  
The Uniqueness Theorem

Non-selfadjoint second-order differential operators with a constant delay are studied. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. For this inverse problem the uniqueness theorem is proved.

On Schrödinger's factorization method for Sturm-Liouville operators

1978 ◽  
Vol 80 (1-2) ◽  
pp. 67-84 ◽  
Author(s):  
U.-W. Schmincke
Keyword(s):  
Discrete Spectrum ◽  
Liouville Operator ◽  
Differential Operators ◽  
Factorization Method ◽  
Friedrichs Extension ◽  
First Order ◽  
Sturm Liouville ◽  
Image Position ◽  
Special Case ◽  
Liouville Operators

SynopsisWe consider the Friedrichs extension A of a minimal Sturm-Liouville operator L0 and show that A admits a Schrödinger factorization, i.e. that one can find first order differential operators Bk with where the μk are suitable numbers which optimally chosen are just the lower eigenvalues of A (if any exist). With the help of this theorem we derive for the special case L0u = −u″ + q(x)u with q(x) → 0 (|x| → ∞) the inequalityσd(A) being the discrete spectrum of A. This inequality is seen to be sharp to some extent.

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