Finite Spectrum of Sturm–Liouville Problems with Transmission Conditions Dependent on the Spectral Parameter. (2nd January 2023)

• Record Type: Journal Article
• Authors: Zhang, Na; Ao, Ji-Jun
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 1(2023)
• Page Start: 21
• Page End: 35
• Publication Date: 2023-01-02
• Subjects: Primary 34L10 -- 34B20 -- Secondary 47A45; eigenvalues -- finite spectrum -- Sturm–Liouville problems -- transmission conditions with spectral parameter; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2150641
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we mainly study the finite spectrum of Sturm–Liouville problems with transmission conditions dependent on the spectral parameter. By analyzing on the characteristic function, we prove that this kind of Sturm–Liouville problems consist of finite number of eigenvalue and these finite eigenvalues can be located anywhere in the complex plane. It is illustrated that the number of eigenvalues not only depends on the partition of the domain interval, but also depends on the transmission conditions dependent on the spectral parameter and the boundary conditions.