Oscillation of Half-Linear Differential Equations with Delay

Abstract EN

We study the half-linear delay differential equation (r(t)Φ(x'(t)))'+c(t)Φ(x(τ(t)))=0, Φ(x):=|x|p-2x, p>1.

We establish a new a priori bound for the nonoscillatory solution of this equation and utilize this bound to derive new oscillation criteria for this equation in terms of oscillation criteria for an ordinary half-linear differential equation.

The presented results extend and improve previous results of other authors.

An extension to neutral equations is also provided.