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

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... bounded, and thus, our results are supplements to some well-known periodic problems. Finally, we give one example to illustrate our main results.