Oscillation of linear third-order impulsive difference equations with variable coefficients

Abstract

Abstract The present work discusses the qualitative behaviour of solutions of third-order difference equations of the form: $$\begin{aligned} w(l+3)+a(l)w(l+2)+b(l)w(l+1)+c(l)w(l)=0,\,l\ne \theta _{k},\,l\ge l_{0} \end{aligned}$$ w ( l + 3 ) + a ( l ) w ( l + 2 ) + b ( l ) w ( l + 1 ) + c ( l ) w ( l ) = 0 , l ≠ θ k , l ≥ l 0 subject to the impulsive condition $$\begin{aligned} w(\theta _{k})=\alpha _{k} w(\theta _{k}-1),\, k\in {\mathbb {N}}. \end{aligned}$$ w ( θ k ) = α k w ( θ k - 1 ) , k ∈ N . Our state of the art is the inequality technique under the control of fixed moments of impulsive effect. We give some numerical examples to illustrate our findings.

Keywords

• Oscillation
• Nonoscillation
• Third-order difference equation
• Discrete impulse