Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Abstract

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Symmetry and Its Importance in the Oscillation of Solutions of Differential Equations

“…for all positive ξ. Lemma 2. [19] If the function ξ satisfies ξ (m) (y) > 0, m = 0, 1, ..., n, and ξ (n+1) (y) < 0 for y ≥ y 0 , then ξ(y)…”

Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms

“…In particular, it is a necessary and invaluable issue, either theoretically or practically, to probe into neutral differential equations with distributed deviating arguments. Hence, a scientific study of the qualitative properties of solutions of these equations is proposed for applications, see for example the book [7,8] and the papers [9][10][11][12][13][14][15].…”

Oscillatory Solutions to Neutral Delay Differential Equations

“…In recent years, and in context of oscillation theory, many studies have been devoted to the oscillation conditions for non-linear delay differential equations; the reader can refer to [8][9][10][11][12][13][14][15][16].…”