AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$
Δ
(
Δ
u
(
k
-
1
)
p
-
2
Δ
u
(
k
-
1
)
)
+
a
(
k
)
u
(
k
)
p
-
2
u
(
k
)
=
0
with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.