Abstract
Abstract
The paper is concerned with the Neumann eigenvalues for second-order Sturm–Liouville difference equations. By analyzing the new discriminant function, we show the interlacing properties between the periodic, antiperiodic, and Neumann eigenvalues. Moreover, when the potential sequence is symmetric and symmetric monotonic, we show the order relation between the first Dirichlet eigenvalue and the second Neumann eigenvalue, and prove that the minimum of the first Neumann eigenvalue gap is attained at the constant potential sequence.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference26 articles.
1. Ashbaugh, M.S., Benguria, R.D.: Optimal lower bound for the gap between the first two eigenvalues of one-dimensional Schrodinger operators with symmetric single-well potentials. Proc. Am. Math. Soc. 105, 419–424 (1989)
2. Ashbaugh, M.S., Benguria, R.D.: Some eigenvalue inequalities for a class of Jacobi matrices. Linear Algebra Appl. 136, 215–234 (1990)
3. Atkinson, F.V.: Discrete and Continuous Boundary Problems. Academic Press, New York (1964)
4. Birkhoff, G., Rota, G.C.: Ordinary Differential Equations. Wiley, New York (1989)
5. Borg, G.: Eine Umkehrung der Sturm–Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte. Acta Math. 78, 1–96 (1946)