An oscillation criterion for discrete trigonometric systems

作者：Dosly Ondrej; Elyseeva Julia^*

来源：Journal of Difference Equations and Applications, 2015, 21(12): 1256-1276.

DOI：10.1080/10236198.2015.1070842

• trigonometric difference systems
• focal points
• symplectic SVD
• oscillation criteria
• comparative index

In this paper, we investigate oscillation properties of discrete trigonometric systems whose coefficients matrices are simultaneously symplectic and orthogonal. The main result generalizes a necessary and sufficient condition of non-oscillation of trigonometric systems proved by M. Bohner and O. Doly (J. Differential Equations 163 (2000), pp. 113-129) in the case when the block in the upper right corner of the coefficient matrix is symmetric and positive definite. Now, we present this oscillation criterion for an arbitrary trigonometric system. The obtained results are applied to formulate a necessary and sufficient condition for non-oscillation of even-order Sturm-Liouville difference equations.

• 出版日期2015