Solvability theorems for an inverse nonself-adjoint Sturm-Liouville problem with nonseparated boundary conditions
type: Item
instance of: scholarly article
title: Solvability theorems for an inverse nonself-adjoint Sturm-Liouville problem with nonseparated boundary conditions
zbMATH Open document ID: 1328.34019
DOI: 10.1134/S0012266115060026
author: Ya. T. Sultanaev
author: V. A. Sadovnichy
author: A. M. Akhtyamov
published in: Differential Equations
publication date: 2015-09-28T00:00:00Z
review text: Let \(\{\lambda_k\}\) be the eigenvalues of the boundary value problem \[ -y''+q(x)y=\lambda y, \] \[ y'(0)+a_{11}y(0)+a_{12}y(\pi)=y'(\pi)+a_{21}y(0)+a_{22}y(\pi)=0. \] The following inverse problem is solved: given three eigenvalues \(\lambda_1, \lambda_2, \lambda_3\), construct three coefficients \(a_{12}, a_{21}, a_{22}\), provided the function \(q(x)\) and the coefficient \(a_{11}\) are known a priori.
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 6485725
zbMATH Keywords: differential operators
zbMATH Keywords: nonseparated boundary conditions
zbMATH Keywords: inverse spectral problem
reviewed by: V. A. Yurko
MaRDI profile type: Publication
cites work: Q4183612
cites work: Q3695595
cites work: Q3447126
cites work: Inverse oscillation theory for Sturm–Liouville problems with non-separated boundary conditions
cites work: The inverse Sturm-Liouville problem: Uniqueness theorems and counterexamples
cites work: Q4081634
cites work: Q3767650
cites work: An inverse problem for the Sturm-Liouville operator with nonseparable self-adjoint boundary conditions
cites work: The inverse spectral problem for differential operators with nonseparated boundary conditions
cites work: Q5521760
cites work: Analogues of Borg's uniqueness theorem in the case of nonseparated boundary conditions
cites work: Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition
cites work: Reconstruction formula for the potential function of Sturm–Liouville problem with eigenparameter boundary condition
cites work: Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions
cites work: Q5728657
cites work: Solution of a class of inverse boundary-value Sturm-Liouville problems
cites work: The inverse spectral problem for pencils of differential operators
cites work: Inverse eigenvalue problems for perturbed spherical Schrödinger operators
cites work: Inverse problems for Sturm-Liouville operators with potentials in Sobolev spaces: uniform stability
description: scientific article; zbMATH DE number 6485725