Partial Inverse Problems for the Sturm–Liouville Operator on a Star-Shaped Graph with Different Edge Lengths

2018 ◽  
Vol 73 (2) ◽  
Author(s):  
Natalia Pavlovna Bondarenko ◽  
Chuan-Fu Yang
Keyword(s):  
Inverse Problems ◽  
Liouville Operator ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph

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 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.

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.

Inverse problems for the impulsive Sturm–Liouville operator with jump conditions

2018 ◽  
Vol 27 (10) ◽  
pp. 1442-1450 ◽  
Author(s):  
Yasser Khalili ◽  
Nematollah Kadkhoda ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problems ◽  
Liouville Operator ◽  
Jump Conditions ◽  
Sturm Liouville
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