Oscillation result for half-linear delay difference equations of second-order

Abstract

<abstract><p>In this paper, we obtain the new single-condition criteria for the oscillation of second-order half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.</p></abstract>

Existence and controllability results for neutral fractional Volterra-Fredholm integro-differential equations

“…Moreover, recent research explores oscillation in second-order impulsive systems [42], numerical anal-ysis of fractional order discrete Bloch equations [33], and oscillation results for half-linear delay difference equations of second order [22]. Contributions by Santra and Scapellato offer insights into necessary and sufficient conditions for the oscillation of second-order differential equations with mixed several delays [44], while Moaaz et al investigate the asymptotic behavior of even-order noncanonical neutral differential equations [35].…”

Oscillatory Properties of Third-order Neutral Delay Difference Equations

“…and established some criteria for the oscillation of certain third-order DEs using comparison principles with a suitable couple of first order DEs. For more about the related works the authors are refer [10][11][12][13][14][15][16][17] to the readers.…”

Application of Fourier Transform to Study Hyers-Ulam Stability of Linear Differential Equations

“…where a is a four times continuously differentiable function, h, f, u and g are scalars and ξ(e) is the continuously differentiable function. There are many related works [12][13][14][15][16][17][18][19] and the reference references cited therein. The outline of the paper as follows: In Section 2, some definitions are introduced.…”