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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.

New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments

Attia Emad R., El-Matary Bassant M., Chatzarakis George E.

Opuscula Mathematica

2022

Vol. 42, no. 6

769--791

In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving lim sup, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.

New aspects for the oscillation of first-order difference equations with deviating arguments

Attia Emad R., El-Matary Bassant M.

Opuscula Mathematica

2022

Vol. 42, no. 3

393--413

We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.