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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.

On the qualitative behavior of the solutions to second-order neutral delay differential equations

Chatzarakis George E., Santra Shyam S.

Fasciculi Mathematici

2020

nr 64

43--56

In this paper, we study the qualitative behavior of the solutions to second-order neutral delay differential equations of the form (r(t) ((x(t) + p(t)x(τ (t)))′)γ)′ + q(t)f (x(σ(t))) = 0. Our main tool is Lebesgue’s dominated convergence theorem. Examples illustrating the applicability of the results are also given.

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.