Oscillatory properties of third order neutral dynamic equations

Abstract

Oscillatory properties of third-order half-linear neutral dynamic equations were investigated in this paper. Some conditions are obtained to ensure the oscillation of all solutions of a neutral dynamic equation with several coefficients and several variable delays, t ∈ [t0, ∞)𝕋, where γ > 0 is a quotient of odd positive integers, , and , and 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]).…”

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.…”