International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 8, Pages 34232, 7 p.
doi:10.1155/IJMMS/2006/34232

Oscillation of solutions of impulsive neutral difference equations with continuous variable

Abstract

We obtain sufficient conditions for oscillation of all solutions of the neutral impulsive difference equation with continuous variable Δτ(y(t)+p(t)y(t−mτ))+Q(t)y(t−lτ)=0, t≥t0−τ, t≠tk, y(tk+τ)−y(tk)=bky(tk), k∈ℕ(1), where Δτ denotes the forward difference operator, that is, Δτz(t)=z(t+τ)−z(t), p(t)∈C([t0−τ,∞),ℝ), Q(t)∈C([t0−τ,∞),(0,∞)), m, l are positive integers, τ>0 and bk are constants, 0≤t0<t1<t2<⋯<tk<⋯ with limk→∞tk=∞.