Author:
Cai Jinming,Li Shuang,Li Kun
Abstract
<p>We investigate the Sturm-Liouville (S-L) operator with boundary and transfer conditions dependent on the eigen-parameter. By utilizing interval partitioning and factorization techniques of characteristic function, it is proven that this problem has a finite number of eigenvalues when the coefficients of the equation meet certain conditions, and some conditions for determining the number of eigenvalues are provided. The results indicate that the number of eigenvalues in this problem varies when the transfer conditions depend on the eigen-parameter. Furthermore, the equivalence between this problem and matrix eigenvalue problems is studied, and an equivalent matrix representation of the S-L problem is presented.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference36 articles.
1. J. Weidmann, Spectral theory of ordinary differential operators, Springer, 1987. https://doi.org/10.1007/BFb0077960
2. C. Bennewitz, M. Brown, R. Weikard, Spectral and scattering theory for ordinary differential equations, Springer, 2020. https://doi.org/10.1007/978-3-030-59088-8
3. A. M. Krall, E. Bairamov, Ö. Çakar, Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, J. Differ. Equations, 151 (1999), 252–267. https://doi.org/10.1006/jdeq.1998.3519
4. X. Zhu, Z. Zheng, K. Li, Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with boundary conditions dependent on the eigenparameter, Acta Math. Sin Engl. Ser., 39 (2023), 2164–2180. https://doi.org/10.1007/s10114-023-1413-6
5. S. Goyal, S. A. Sahu, S. Mondal, Modelling of love-type wave propagation in piezomagnetic layer over a lossy viscoelastic substrate: Sturm-Liouville problem, Smart Mater. Struct., 28 (2019), 057001. https://doi.org/10.1088/1361-665X/ab0b61