Affiliation:
1. Department of Mathematics, Taiyuan University , Taiyuan , 030032 , P. R. China
2. School of Mathematics and Statistics, Huanghuai University , Zhumadian , 463000 , P. R. China
Abstract
Abstract
In this article, by using critical point theory, we prove the existence of multiple
T
T
-periodic solutions for difference equations with the mean curvature operator:
−
Δ
(
ϕ
c
(
Δ
u
(
t
−
1
)
)
)
+
q
(
t
)
u
(
t
)
=
λ
f
(
t
,
u
(
t
)
)
,
t
∈
Z
,
-\Delta ({\phi }_{c}\left(\Delta u\left(t-1)))+q\left(t)u\left(t)=\lambda f\left(t,u\left(t)),\hspace{1em}t\in {\mathbb{Z}},
where
Z
{\mathbb{Z}}
is the set of integers. As a
T
T
-periodic problem, it does not require the nonlinear term is unbounded or bounded, and thus, our results are supplements to some well-known periodic problems. Finally, we give one example to illustrate our main results.