Oscillation and Asymptotic Behavior of Second Order Half Linear Neutral Dynamic Equations

Abstract

The oscillation property of the second order half linear dynamic equation was studied, some sufficient conditions were obtained to ensure the oscillation of all solutions of the equation. The results are supported by illustrative examples.

Almost Oscillatory Solutions of a Three-Dimensional Half-Linear Neutral differential System of the Second Order

“…Differential equations are one of the most important topics in mathematics due to their many applications [1][2][3]. NDEs represent one of these equations that have been of interest to many researchers, especially in the subject of oscillation and the behavior of the solution (see [4][5][6][7][8]). The oscillation properties of systems of differential equations, whether they are ordinary, delay, neutral, difference equations, or dynamic equations is the main concern of study (see [9][10]).…”

“…The oscillation properties of systems of differential equations, whether they are ordinary, delay, neutral, difference equations, or dynamic equations is the main concern of study (see [9][10]). A few of these oscillation properties have been investigated in the system of NDEs, (see [11][12][13]). Agarwal et al [14], discussed the delay of nonlinear differential equation system as follows:…”

Oscillation and Asymptotic Behavior of Three-Dimensional Third-Order Delay Systems

“…Numerous research studies and theses have been written about the oscillation and asymptotic behavior of DDEs with various orders. Te reader can see these research studies in [10][11][12][13][14][15][16][17][18] and the references cited therein. However, there are few studies (books or papers) that discuss the concept of oscillation for solving delay equations such as Ladde et al [7,19], Foltynska [20], Agarwal et al [21], Mohamad and Abdulkareem [22], Abdulkareem et al [23], Akın-Bohner et al [24], Špániková [25], and the references cited therein.…”