Multiplicities and relative position of eigenvalues of a quadratic pencil of Sturm-Liouville operators

2000 ◽  
Vol 67 (3) ◽  
pp. 309-319 ◽  
Author(s):  
I. M. Nabiev
Keyword(s):  
Relative Position ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals Partial inverse problems for quadratic differential pencils on a graph with a loop

2020 ◽  
Vol 28 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Natalia P. Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Spectral Characteristics ◽  
The Other ◽  
Boundary Edge ◽  
Partial Inverse ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

AbstractIn this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.

On the Inverse Problem for a Quadratic Pencil of Sturm-Liouville Operators with Periodic Potential

2005 ◽  
Vol 41 (3) ◽  
pp. 310-318 ◽  
Author(s):  
B. A. Babadzhanov ◽  
A. B. Khasanov ◽  
A. B. Yakhshimuratov
Keyword(s):  
Inverse Problem ◽  
Periodic Potential ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals Partial inverse problems for Sturm–Liouville operators on trees

2017 ◽  
Vol 147 (5) ◽  
pp. 917-933 ◽  
Author(s):  
Natalia Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Sets ◽  
Spectral Problems ◽  
Partial Inverse ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Liouville Operators

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 functions on a tree with b external edges. Constructive solutions, based on the method of spectral mappings, are provided for the considered inverse problems.

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