Oscillations and Asymptotic Behaviour of Solutions for Second Order Neutral Delay Differential Equations

Abstract

Oscillatory and asymptotic behaviour of solutions of second order nonlinear neutral-delay differential equations of the form

(x(t)-ΣP₁ x(t-Ï„₁))" + Q(t)x^α(t-α)=0,

where Ï„₁, P₁(i=1, 2, ......., n) and σ ∈ R⁺, Q ∈ C([t₀, ∞), R⁺),

t₀≥0 and α > 0 is a ratio of odd integers, are studied. The results of this paper generalize and supplement certain recent results due to Peixuan.