Multiple periodic solutions for discrete boundary value problem involving the mean curvature operator

Abstract

In this article, by using critical point theory, we prove the existence of multiple TT-periodic solutions for difference equations with the mean curvature operator: −Δ(ϕc(Δu(t−1)))+q(t)u(t)=λf(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 TT-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.

Keywords

• difference equations
• mean curvature operator
• periodic solutions
• critical point theory
• 39a27
• 39a70