Abstract
By employing primary algebraic techniques, we establish a necessary and sufficient condition for the existence of periodic solutions for a type of linear difference equations with distributed delay of the form
Δ
x
(
n
)
=
∑
k
=
-
d
0
Δ
k
ζ
(
n
+
1
,
k
-
1
)
x
(
n
+
k
-
1
)
,
n
≥
1
.
(*)
Our approach is based on constructing an adjoint equation for (*) and proving that (*) and its adjoint equation have the same number of linearly independent periodic solutions.
AMS Subject Classification:
39A11.