Title: Oscillation theorems and asymptotic behaviour of certain third-order neutral differential equations with distributed deviating arguments

Authors: Yibing Sun; Yige Zhao

Addresses: School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, China ' School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, China

Abstract: The purpose of this paper is to study the oscillation criteria for a class of third-order neutral differential equations with distributed deviating arguments
[b(t)((a(t)(z^′(t))^α1)^′)^α2]^′ + ∫d c q(t,ξ)ƒ(x(α(t,ξ)))dξ = 0, t ≥ t₀
where z(t) = x(t) + ∫n m p(t, ξ)x(τ (t, ξ))dξ and α_i are ratios of positive odd integers, i=1, 2. By using a generalized Riccati transformation and an integral averaging technique, we establish some new theorems, which ensure that all solutions of this equation oscillate or converge to zero. Some examples are given to illustrate our main results.

Keywords: third-order neutral differential equations; distributed deviating arguments; oscillation; asymptotic behaviour; generalised Riccati transformation.

DOI: 10.1504/IJDSDE.2021.115181

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.2, pp.174 - 189

Received: 12 Jan 2019
Accepted: 22 Jun 2019
Published online: 24 May 2021 *

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