Abstract
Let
k
be a nonnegative integer and
c
a real number greater than or equal to 1. We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation
z
n
+
1
=
(
c
z
n
+
z
n
-
k
+
c
-
1
z
n
z
n
-
k
)
/
(
z
n
z
n
-
k
+
c
)
,
n
≥
0
,
with positive initial values
z
-
k
,
z
-
k
+
1
,
⋯
,
z
0
, and show the global asymptotic stability of its positive equilibrium solution.