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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.

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.

Oscillations of equations caused by several deviating arguments

Chatzarakis George E

Opuscula Mathematica

2019

Vol. 39, no. 3

321--353

Linear delay or advanced differential equations with variable coefficients and several not necessarily monotone arguments are considered, and some new oscillation criteria are given. More precisely, sufficient conditions, involving limsup and liminf, are obtained, which essentially improve several known criteria existing in the literature. Examples illustrating the results are also given, numerically solved in MATLAB.

Improved iterative oscillation tests for first-order deviating differential equations

Chatzarakis G. E, Jadlovska I.

Opuscula Mathematica

2018

Vol. 38, no. 3

327--356

In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing lim sup and lim inf on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.