Oscillation of Second Order Nonlinear Neutral Differential Equations

Abstract

Abstract:The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.

Nonoscillatory Properties of Fourth Order Nonlinear Neutral Differential equation

“…Many researchers have discussed and investigated the oscillatory and asymptotic behaviour solution of NDE in their works for more details see the references listed therein [1][2][3][4][5][6][7][8][9][10].…”

“…Eq. ( 3) may be written as well as the 𝔇 (4) (𝜉) ≥ 𝑚|𝒬(𝜉)|𝒫(𝓋(𝜉)) ≥ 𝑚|𝒬(𝜉)|𝔇(𝓋(𝜉)) (11) By substituting (10) in (11) we get 𝔇 (4) In terms of condition (8) and Lemma 2, it follows that the last inequality is impossible to have eventually positive solution, this is incongruous. Case 2: We claim that lim inf 𝜉→∞ 𝒫(𝜉) = 0, otherwise lim inf 𝜉→∞ 𝒫(𝜉) = 𝑙 1 > 0.…”

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.…”