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  • Author: Robert Mařík x
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Abstract

In this paper we derive oscillation criteria for the second order half-linear neutral differential equation
[r(t)Φ(z(t))]+c(t)Φ(x(σ(t)))=0,z(t)=x(t)+b(t)x(τ(t)),

where Φ(t) = |t|p−2 t, p ≥ 2, is a power type nonlinearity. We improve recent results published in the literature by obtaining better oscillation constants and removing the usual condition σ(τ(t)) = τ(σ(t)). Two methods (comparison method and Riccati equation method) are used.

Abstract

Neutral differential equations are one of the most important extensions of classical ordinary differential equations and aim to give a better explanation for modeling phenomena where ordinary differential equations are insufficient. Naturally, all the questions studied in the scope of ordinary differential equations attracted the attention also for neutral differential equations. In this paper we study the oscillatory properties of second order half-linear neutral differential equations. We present oscillation criteria derived using a new approach. This approach allows us to reduce common restrictions on the deviations in arguments which are present in the currently known results of this type.