Opuscula Math. 41, no. 5 (2021), 613-627
https://doi.org/10.7494/OpMath.2021.41.5.613
Opuscula Mathematica
Oscillation criteria for linear difference equations with several variable delays
Vasileios Benekas
Ábel Garab
Ardak Kashkynbayev
Ioannis P. Stavroulakis
Abstract. We obtain new sufficient criteria for the oscillation of all solutions of linear delay difference equations with several (variable) finite delays. Our results relax numerous well-known limes inferior-type oscillation criteria from the literature by letting the limes inferior be replaced by the limes superior under some additional assumptions related to slow variation. On the other hand, our findings generalize an oscillation criterion recently given for the case of a constant, single delay.
Keywords: oscillation, difference equations, several delays, non-monotone argument, slowly varying function.
Mathematics Subject Classification: 39A21, 39A10.
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- Vasileios Benekas
https://orcid.org/0000-0001-9693-1499- Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
- Ábel Garab (corresponding author)
- https://orcid.org/0000-0001-9693-1923
- Department of Mathematics, University of Klagenfurt, Universitätsstraße 65-67, A-9020 Klagenfurt, Austria
- Ardak Kashkynbayev
- https://orcid.org/0000-0002-1338-2058
- Department of Mathematics, Nazarbayev University, Qabanbay Batyr Avenue, 53, 010000 Nur-Sultan, Kazakhstan
- Ioannis P. Stavroulakis
- https://orcid.org/0000-0002-4810-0540
- Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
- Communicated by Josef Diblík.
- Received: 2021-08-04.
- Accepted: 2021-08-20.
- Published online: 2021-09-30.
