On the oscillation of third-order quasi-linear delay differential equations

Abstract

ABSTRACT. The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equationwhere α > 0,dt < ∞ and τ (t) ≤ t. We establish a new condition which guarantees that every solution of (E) is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.

Oscillatory Behavior of Third-Order Quasi-Linear Neutral Differential Equations

“…Using comparison theorems and the Riccati technique, we established criteria to check the oscillation under fewer restrictions, and compared this with some results published in the literature. Our results are an extension of and complement to existing results in some previous studies, such as [15,27,29].…”

“…See, for example, [5,6] and the references cited therein. Compared to the development of the oscillation for the second-order equations, the oscillation for third-order equations has received considerably less attention from researchers; see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Oscillatory and asymptotic properties of third-order quasilinear delay differential equations

“…Using a different technique based on reducing the studied equation into a first-order Riccati-type inequality, which is generally considered as one of the most valuable tools in the oscillation theory, Li et al [15] provided the following criterion for property A of (1.1).…”

On property (B) of higher order delay differential equations

“…imposed on the coefficient r(t), see e.g. [5], [15], [21] and even r(t) ≡ 1 in [14]. The main novelty of this paper consists in relaxing this nonotonicity condition.…”