Singular comparison theorems for symplectic difference systems

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Authors

DOŠLÝ Ondřej ELYSEEVA Julia

Year of publication 2014
Type Article in Periodical
Magazine / Source J. Difference Equ. Appl.
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1080/10236198.2014.908862
Field General mathematics
Keywords symplectic difference system; recessive solution; Riccati equation; comparative index
Attached files
Description We present new relations connecting the number of focal points of conjoined bases of eventually disconjugate symplectic difference systems with different coefficient matrices which obey a majorant condition at $\infty.$ For the case of controllable (near $\infty$) symplectic systems we investigate connections between the number of focal points of their recessive solutions. The consideration is based on the concept of minimal and maximal solutions of the associated Riccati matrix difference equations and the comparative index theory for discrete symplectic systems.
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