Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type

Abstract

In this article, some new oscillation criterion for the second order Emden-Fowler functional differential equation of neutral typewhere), α > 0 and β > 0 are established. Our results improve some well-known results which were published recently in the literature. Some illustrating examples are also provided to show the importance of our results.

New criteria for oscillation of nonlinear neutral differential equations

“…Secondly, we present a new result for oscillation of (1.1) by using the technique of Riccati transformation, which improves the related results reported in [23,28]. In order to show the importance of our results, we introduce two examples and compare the results in this paper with the previous results.…”

“…have been studied by Baculikova and Dzurina in [6] when γ ≥ β, σ (t) and τ (t) are nondecreasing, τ (σ (t)) = σ (τ (t)). By using the Riccati transformation technique, in [23,28,30], the oscillatory properties of solutions of the equation…”

“…Zeng et al [30] used the technique of Riccati transformation to obtain oscillation conditions for (1.4), which improves the results in [23]. Under a more general case, namely for all γ > 0 and β > 0, Wu et al [28] studied the oscillation criteria of equation (1.4). The purpose of this work is to contribute to the development of the oscillation theory of second order nonlinear equations with delay argument.…”

Oscillation for a generalized neutral Emden-Fowler equation with damping and distributed delay

“…Subsequently, by using the similar method, Zeng et al 21 obtained the oscillation for (2) with α β > 0 or 0 < α β. Further, by using the generalized Riccati inequality, Wu et al 22 studied the oscillation of (2) for α, β > 0.…”

Oscillation criteria for second-order quasi-linear neutral functional differential equation

“…One of these equations has got a lot of attention [9,14,20], the quasi-linear neutral delay equation…”