Oscillation of Second Order Quasi-linear Neutral Delay Differential Equations

Abstract

In this paper, by employing generalized Riccati transformation and some specific analytical skills, we will establish some new oscillation criteria for the second order quasi-linear neutral delay equation of the form $$ (r(t)|z^{'}(t)|^{\alpha-1}z^{'}(t))^{'}+q(t)f(x(\sigma(t)))=0,\ \ t\geq t_0, $$ where z(t)=x(t)+p(t)x(τ(t)), −1 < p₁ ≤ p(t) ≤ 0, q(t) > 0, α > 0. The results obtianed essentially improve and extent the results in the cited literature