On the Oscillation of Second-Order Neutral Delay Differential Equations

Abstract

Some new oscillation criteria for the second-order neutral delay differential equation (r(t)z′(t))′+q(t)x(σ(t))=0, t≥t0 are established, where ∫t0∞(1/r(t))dt=∞, z(t)=x(t)+p(t)x(τ(t)), 0≤p(t)≤p0<∞, q(t)>0. These oscillation criteria extend and improve some known results. An example is considered to illustrate the main results.