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

Abstract

By introducing auxiliary functions, we investigate the oscillation of a class of second-order sub-half-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,whereβ>α>0,  z(t)=x(t)+λ(t)x(τ(t)).  Several oscillation criteria for the above equation are established in both the case0≤λ(t)≤1and 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.