## Riccati transformation and nonoscillation criterion for linear difference equations

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- by Kōdai Fujimoto, Petr Hasil and Michal Veselý PDF
- Proc. Amer. Math. Soc.
**148**(2020), 4319-4332 Request permission

## Abstract:

We consider a general class of linear difference equations. Using a variation of the discrete Riccati method, we obtain a straightforward nonoscillation criterion for the treated equations. In contrast to a number of known criteria, we do not need to consider any auxiliary sequences. We use the coefficients of the treated equations directly. To illustrate the novelty and the usage of the presented criterion, we provide corollaries and examples.## References

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## Additional Information

**Michal Veselý**- Affiliation: Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37 Brno, Czech Republic; Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37 Brno, Czech Republic; Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37 Brno, Czech Republic
- Email: kfujimoto@outlook.com, hasil@mail.muni.cz, michal.vesely@mail.muni.cz
- Received by editor(s): September 24, 2019
- Received by editor(s) in revised form: February 12, 2020
- Published electronically: June 1, 2020
- Additional Notes: This research was supported by Grant GA20-11846S of the Czech Science Foundation.

The third author is the corresponding author. - Communicated by: Mourad Ismail
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 4319-4332 - MSC (2010): Primary 39A06, 39A21; Secondary 39A10, 39A12, 47B39
- DOI: https://doi.org/10.1090/proc/15072
- MathSciNet review: 4135300