Inverse problem for a fourth-order differential operator with nonseparated boundary conditions
type: Item
instance of: scholarly article
title: Inverse problem for a fourth-order differential operator with nonseparated boundary conditions
zbMATH Open document ID: 1415.34046
DOI: 10.1134/S0012266118100063
author: Ya. T. Sultanaev
author: V. A. Sadovnichy
author: A. M. Akhtyamov
published in: Differential Equations
publication date: 2019-03-27T00:00:00Z
review text: Boundary value problems are considered for the differential equation \[ y^{(4)}+p_2(x)y''+p_1(x)y'+p_0(x)y=\lambda y,\; x\in (0,1) \] with nonseparated boundary conditions. The authors study the inverse problem of recovering coefficients of the boundary conditions from the given eigenvalues provided that the functions \(p_0(x)\), \(p_1(x)\) and \(p_2(x)\) are known a priori. Uniqueness theorems are formulated for this class of inverse problems. Regrettably, these results are wrong. The reason is that the authors use incorrectly Leibenson's uniqueness result, because the specification of the considered spectral data does not uniquely determines the operator. The correct statement and solution of the inverse spectral problem for arbitrary order differential operators are presented in [\textit{V. Yurko}, Method of spectral mappings in the inverse problem theory. Utrecht: VSP (2002; Zbl 1098.34008)].
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34B09
zbMATH DE Number: 7043432
zbMATH Keywords: differential equations
zbMATH Keywords: inverse problems
zbMATH Keywords: uniqueness result
reviewed by: V. A. Yurko
MaRDI profile type: Publication
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full work available at URL: s0012266118100063
OpenAlex ID: W2901536183
description: scientific article; zbMATH DE number 7043432