Oscillation of Certain Second-Order Sub-Half-Linear Neutral Impulsive Differential Equations

By introducing auxiliary functions, we investigate the oscillation of a class of second-order subhalf-linear neutral impulsive differential equations of the form r t φβ z′ t ′ p t φα x σ t 0, t / θk,Δφβ z′ t |t θk qkφα x σ θk 0,Δx t |t θk 0, where β > α > 0, z t x t λ t x τ t . Several oscillation criteria for the above equation are established in both the case 0 ≤ λ t ≤ 1 and the case −1 < −μ ≤ λ t ≤ 0, which generalize and complement some existing results in the literature. Two examples are also given to illustrate the effect of impulses on the oscillatory behavior of solutions to the equation.