Oscillation criterion for discrete trigonometric systems

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Authors

DOŠLÝ Ondřej ELYSEEVA Julia

Year of publication 2015
Type Article in Periodical
Magazine / Source J. Difference Equ. Appl.
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1080/10236198.2015.1070842
Field General mathematics
Keywords Trigonometric system; oscillation criterion; focal points; symplectic SVD; comparative index
Attached files
Description 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 nonoscillation of trigonometric systems proved by M.~Bohner and O.~Do\v{s}l\'y (J. Differential Equations 163 (2000), 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 nonoscillation of even-order Sturm-Liouville difference equations
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