Abstract
AbstractThe 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.
Funder
University Grants Commission
Publisher
Springer Science and Business Media LLC