Browsing by Subject "non-monotone argument"

Now showing 1 - 4 of 4

Access status: Open Access ,
Improved iterative oscillation tests for first-order deviating differential equations
(Wydawnictwa AGH, 2018) Chatzarakis, George E.; Jadlovská, Irena
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.
Access status: Open Access ,
New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments
(Wydawnictwa AGH, 2022) Attia, Emad R.; El-Matary, Bassant M.; Chatzarakis, George E.
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.
Access status: Open Access ,
Oscillation criteria for linear difference equations with several variable delays
(Wydawnictwa AGH, 2021) Benekas, Vasileios; Garab, Ábel; Kashkynbayev, Ardak; Stavroulakis, Ioannis P.
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.
Access status: Open Access ,
Oscillations of equations caused by several deviating arguments
(Wydawnictwa AGH, 2019) Chatzarakis, George E.
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 $\lim\sup$ and $\lim\inf$, are obtained, which essentially improve several known criteria existing in the literature. Examples illustrating the results are also given, numerically solved in MATLAB.