Inverse spectral problems for differential pencils on a graph with a rooted cycle

Yurko, V. A.

doi:10.1080/17415977.2015.1135329

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Uniqueness Theorem For Inverse Problem1

Introduction1

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Cited by 3 publications

(2 citation statements)

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“…For simplicity, we assume that α m = 0. Using (10) and (11) for j = m, we conclude that The index m denotes the connection with the inverse problem, that consists in recovering the pencil coefficients on the edge e m , i.e. on the loop.…”

Section: Uniqueness Theorem For Inverse Problemmentioning

confidence: 99%

See 1 more Smart Citation

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

Bondarenko¹,

Shieh²

2018

Preprint

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In this paper, partial inverse problems for the quadratic pencil of Sturm-Liouville operators on a graph with a loop were 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 the partial inverse problems.

show abstract

Section: Uniqueness Theorem For Inverse Problemmentioning

confidence: 99%

“…Inverse problems for quadratic pencils on a finite interval were studied in [4][5][6][7][8], however, some questions still remain open. In recent years, inverse spectral problems for differential pencils on graphs have attracted much attention [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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

Bondarenko¹,

Shieh²

2018

Preprint

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show abstract

A Partial Inverse Problem for the Differential Pencil on a Star-Shaped Graph

Bondarenko

2017

Results Math

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

Bondarenko

Shieh

2020

Journal of Inverse and Ill-Posed Problems

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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.

show abstract

Inverse spectral problems for differential pencils on a graph with a rooted cycle

Cited by 3 publications

References 26 publications

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

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

A Partial Inverse Problem for the Differential Pencil on a Star-Shaped Graph

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

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