1. On the jth Eigenvalue of Sturm–Liouville Problem and the Maslov Index.
- Author
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Hu, Xijun, Liu, Lei, Wu, Li, and Zhu, Hao
- Subjects
- *
EIGENVALUES , *BOUNDARY layer (Aerodynamics) , *MONODROMY groups - Abstract
In the previous papers (Hu et al. in J Differ Equ 266(7):4106–4136, 2019; Kong et al. in J Differ Equ 156(2):328–354, 1999), the jump phenomena of the j-th eigenvalue were completely characterized for Sturm–Liouville problems. In this paper, we show that the jump number of these eigenvalue branches is exactly the Maslov index for the path of corresponding boundary conditions. Then we determine the sharp range of the jth eigenvalue on each layer of the space of boundary conditions. Finally, we prove that the graph of monodromy matrix tends to the Dirichlet boundary condition as the spectral parameter goes to - ∞ . [ABSTRACT FROM AUTHOR]
- Published
- 2022
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