An Inverse Spectral Problem of Sturm–Liouville Problems with Transmission Conditions

2020 ◽  
Vol 17 (5) ◽  
Author(s):  
Ji-jun Ao ◽  
Liang Zhang
Keyword(s):  
Spectral Problem ◽  
Inverse Spectral Problem ◽  
Transmission Conditions ◽  
Sturm Liouville ◽  
Inverse Spectral

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.

Inverse spectral problem for the Sturm Liouville equation

2003 ◽  
Vol 19 (1) ◽  
pp. 235-252 ◽  
Author(s):  
B M Brown ◽  
V S Samko ◽  
I W Knowles ◽  
M Marletta
Keyword(s):  
Spectral Problem ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Sturm Liouville ◽  
Inverse Spectral

scholarly journals An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
I. Dehghani Tazehkand ◽  
A. Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Spectral Characteristics ◽  
Star Graph ◽  
Dirichlet Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Robin Boundary

We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

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