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

Abstract EN

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, 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.