Half‐inverse problems for the quadratic pencil of the Sturm–Liouville equations with impulse

2020 ◽  
Vol 37 (1) ◽  
pp. 915-924
Author(s):  
Rauf Amirov ◽  
Abdullah Ergun ◽  
Sevim Durak
Keyword(s):  
Inverse Problems ◽  
Quadratic Pencil ◽  
Sturm Liouville

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 Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Rauf Kh. Amırov ◽  
A. Adiloglu Nabıev
Keyword(s):  
Inverse Problems ◽  
Boundary Value Problem ◽  
Finite Interval ◽  
Boundary Value ◽  
Weyl Function ◽  
Integral Representations ◽  
Asymptotic Formulas ◽  
Linearly Independent ◽  
Quadratic Pencil ◽  
Sturm Liouville

In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.

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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