Geodesic
Existence of Nonconstant Periodic Solutions for a Nonlinear Discrete System Involving the $p$-Laplacian
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : 39A11, 58E50, 70H05, 37J45. 
@article{BMMS_2012_35_2_a12,
     author = {Zhiming Luo and Xingyong Zhang},
     title = {Existence of {Nonconstant} {Periodic} {Solutions} for a {Nonlinear} {Discrete} {System} {Involving} the $p${-Laplacian}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_2_a12/}
}
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Zhiming Luo; Xingyong Zhang. Existence of Nonconstant Periodic Solutions for a Nonlinear Discrete System Involving the $p$-Laplacian. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2012_35_2_a12/