Volume 35 • Number 2 • 2012   • Existence of Nonconstant Periodic Solutions for a Nonlinear Discrete System Involving the $p$-Laplacian Zhiming Luo and Xingyong Zhang Abstract. In this paper, we study the following nonlinear discrete system involving the $p$-Laplacian \begin{equation*} \Delta(\phi_p(\Delta u(n-1)))-a(n) |u(n)|^{p-2}u(n)+ \nabla F(n,u(n))=0, \quad n\in \mathbb{Z}. \end{equation*} By making use of the Linking theorem, we obtain a sufficient condition under which the system has at least one nonconstant periodic solution. 2010 Mathematics Subject Classification: 39A11, 58E50, 70H05, 37J45. Full text: PDF