A partial inverse problem for the differential pencil on a star-shaped graph
type: Item
instance of: scholarly article
title: A partial inverse problem for the differential pencil on a star-shaped graph
zbMATH Open document ID: 1386.34026
author: Natalia Bondarenko
published in: Results in Mathematics
publication date: 2018-01-30T00:00:00Z
review text: The paper deals with the quadratic differential pencil on a star-shaped graph: \[ -y_j''(x_j)+q(x_j) y_j(x_j)+2\lambda p_j(x_j) y_j(x_j)=\lambda^2 y_j(x_j) \] on each edge \(e_j\), \(j = \overline{1, m}\), with standard matching conditions in the internal vertex and with the boundary conditions, depending on the spectral parameter. The so-called partial inverse problems is studied, which consist in recovering the functions \(p_1\), \(q_1\), using a part of the spectrum, while the coefficients on the other edges \(e_j\), \(j = \overline{2, m}\), are known a priori. It is supposed that the given eigenvalues do not coincide with the eigenvalues of the pencils, associated with separate edges. The main results of the paper are the uniqueness theorem for the solution of the inverse problem, and a constructive procedure for solving this problem.
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34B45
zbMATH DE Number: 6832352
zbMATH Keywords: differential pencil
zbMATH Keywords: star-shaped graph
zbMATH Keywords: inverse spectral problem
reviewed by: V. A. Yurko
MaRDI profile type: Publication
full work available at URL: s00025-017-0683-7
OpenAlex ID: W2611630759
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DOI: 10.1007/S00025-017-0683-7
description: scientific article; zbMATH DE number 6832352