Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term

Abstract

New oscillation criteria for the second-order Emden-Fowler delay differential equation with a sublinear neutral term are presented. An essential feature of our results is that oscillation of the studied equation is ensured via only one condition. Furthermore, as opposed to the results by Agarwal et al. criteria can be applied to Emden-Fowler delay differential equations with noncanonical operators and a sublinear neutral term. Our results essentially improve, extend, and simplify some known ones reported in the literature. The results are illustrated with examples. K E Y W O R D S delayed argument, Emden-Fowler differential equation, oscillation, second-order, sublinear neutral term M S C ( 2 0 1 0 ) 34C10, 34K11

Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

“…Two examples are given to illustrate the efficiency of our results. We believe that the proof method and the obtained results may be generalized to the differential equations, such as those in [11,13,18].…”

Oscillation of third-order neutral differential equations with damping and distributed delay

“…Furthermore, we choose H(t, s) = (ts) 2 , k = 2, θ = 2, p = 1 2 , q(t, ζ ) = tζ , φ(t) = t, t 0 = 1. By Theorem 3.1, we obtain h(t, s) = 2, ρ(t) = t 2 -1, q(t) = 3 8 t, P(t) = 3 8 t(t 2 -1)e t and lim sup…”

“…Differential equations arise in modeling situations to describe population growth, biology, economics, chemical reactions, neural networks, and so forth; see, e.g., [2][3][4][5][6][7][8]. In the present paper, we investigate the oscillatory behavior of a third-order neutral differential equation with damping and distributed delay.…”

Amended oscillation criteria for second-order neutral differential equations with damping term

“…This research focused on developing and improving the oscillation criteria for differential equations. References [3][4][5][6][7][8][9] improved the oscillation criteria for noncanonical second-order equations with delay and advanced argument. For canonical second-order delay equations, Refs.…”