Dependence of eigenvalues of Sturm-Liouville problems with eigenparameter-dependent boundary conditions and interface conditions
type: Item
instance of: scholarly article
title: Dependence of eigenvalues of Sturm-Liouville problems with eigenparameter-dependent boundary conditions and interface conditions
zbMATH Open document ID: 1496.34057
author: Yanyan Li
published in: Mediterranean Journal of Mathematics
publication date: 2022-03-21T00:00:00Z
review text: In this paper, the authors study continuous dependence and differential expressions of eigenvalues for the second-order Sturm-Liouville equation \[ -\left ( p(x) y'(x) \right )' + q(x)y =\lambda w(x)y, \quad x \in J = [a,c) \cup (c, b], \tag{1}\] with the boundary conditions \begin{align*} (\alpha_1' \lambda - \alpha_1) y(a) - (\alpha_2' \lambda - \alpha_2) p y'(a) =0, \\ (\beta_1' \lambda + \beta_1) y(b) - (\beta_2' \lambda + \beta_2) p y'(b) =0, \tag{2}\end{align*} and the interface conditions \begin{align*} y(c+) - \alpha_3 y(c-) - \beta_3 p y'(c-) = 0, \\ p y'(c+) - \alpha_4 y(c-) - \beta_4 p y'(c-) = 0. \tag{3}\end{align*} The authors prove that the eigenvalues for the equation depend not only continuously but also smoothly on the parameters of the equation: the coefficients, the boundary conditions, the interface conditions, as well as the endpoints. Finally, the authors list the derivative formulas of eigenvalues with respect to all the parameters.
reviewed by: Gang Meng
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 7493764
zbMATH Keywords: Sturm-Liouville problems
zbMATH Keywords: differential expressions
zbMATH Keywords: eigenparameter-dependent boundary conditions
zbMATH Keywords: interface conditions
zbMATH Keywords: eigenvalues
MaRDI profile type: Publication
full work available at URL: s00009-021-01943-x
OpenAlex ID: W4221123973
cites work: An inverse spectral problem of Sturm-Liouville problems with transmission conditions
cites work: Eigenvalues of Sturm-Liouville problems with discontinuity conditions inside a finite interval
cites work: Sturm-Liouville differential operators in direct sum spaces
cites work: Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions
cites work: Dependence of eigenvalues of a class of fourth-order Sturm-Liouville problems on the boundary
cites work: Singularity of the \(n\)-th eigenvalue of high dimensional Sturm-Liouville problems
cites work: Sturm-Liouville problems on time scales with separated boundary conditions
cites work: Dependence of the \(n\)th Sturm-Liouville eigenvalue on the problem
cites work: Eigenvalues of regular Sturm-Liouville problems
cites work: Dependence of eigenvalues of Sturm-Liouville problems on the boundary
cites work: Eigenvalues of regular fourth‐order Sturm–Liouville problems with transmission conditions
cites work: Dependence of eigenvalues of fourth-order differential equations with discontinuous boundary conditions on the problem
cites work: Eigenvalues of fourth-order boundary value problems with self-adjoint canonical boundary conditions
cites work: Problems for Ordinary Differential Equations with Transmission Conditions
cites work: Two-interval Sturm-Liouville operators in direct sum spaces with inner product multiples
cites work: Eigenvalues of a class of regular fourth-order Sturm-Liouville problems
cites work: Boundary eigenvalue problems for differential equations \(N\eta=\lambda P\eta\) with \(\lambda\)-polynomial boundary conditions
cites work: Regular third-order boundary value problems
cites work: Regular eigenvalue problems with eigenvalue parameter in the boundary condition
cites work: Two-interval Sturm--Liouville operators in modified Hilbert spaces
cites work: Q3110716
cites work: Q5698659
cites work: Eigenvalues of regular self-adjoint Sturm-Liouville problems
cites work: Dependence of eigenvalues of Sturm-Liouville problems with eigenparameter dependent boundary conditions
cites work: Dependence of eigenvalues of Sturm- Liouville problems with interface conditions
cites work: Continuous dependence of the \(n\)-th eigenvalue of self-adjoint discrete Sturm-Liouville problems on the problem
DOI: 10.1007/S00009-021-01943-X
description: scientific article; zbMATH DE number 7493764