On the Oscillation of Solutions of Differential Equations with Neutral Term

Abstract

In this work, new criteria for the oscillatory behavior of even-order delay differential equations with neutral term are established by comparison technique, Riccati transformation and integral averaging method. The presented results essentially extend and simplify known conditions in the literature. To prove the validity of our results, we give some examples.

Oscillatory Behavior of Even-Order Half-Linear Neutral Differential Equations

“…e oscillation problem for neutral di erential (1) has been studied by many authors with various techniques. Most of the results are obtained for the case 0 ≤ h(ι) < ∞, see [1][2][3][4][5][6], h(ι) ≥ 1, see [7,8], and α ≥ 1, see [2,5,6,[8][9][10][11][12]. e purpose of this paper is to extend the main results for α ≤ 1 using the Philos function method.…”

Oscillatory Behavior of Higher-Order Differential Equations with Delay Terms

“…for α > β and τ is an increasing function. If (7) holds for some λ ∈ (0, 1) and ∀H > 0, then all solutions of (1) are oscillatory or tend to zero.…”

“…(author?) [7] established new criteria with regard to the oscillatory behaviour of even order DDEs containing the neutral component by using the comparison approach, the Riccati transformation, and the integral averaging method. All three of these methods are statistical in nature.…”