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Oscillation conditions for difference equations with several variable delays

El-Matary Bassant M., El-Morshedy Hassan A., Benekas Vasileios, Stavroulakis Ioannis P.

Opuscula Mathematica

2023

Vol. 43, no. 6

789--801

A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.

Oscillation criteria for linear difference equations with several variable delays

Benekas Vasileios, Garab Abel, Kashkynbayev Ardak, Stavroulakis Ioannis P.

Opuscula Mathematica

2021

Vol. 41, no. 5

613--627

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.