# American Institute of Mathematical Sciences

August  2013, 6(4): 1065-1076. doi: 10.3934/dcdss.2013.6.1065

## Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential

 1 Institut de Recherche en Mathmatique et Physique 2 Universit Catholique de Louvain, chemin du Cyclotron, 2 3 B-1348 Louvain-la-Neuve

Received  August 2011 Published  December 2012

T-periodic solutions of systems of difference equations of the form\begin{eqnarray*}\Delta \phi[\Delta q(n-1)] = \nabla_q F[n,q(n)] + h(n) \quad (n \in \mathbb{Z})\end{eqnarray*}where $\phi = \nabla \Phi$, with $\Phi$ strictly convex, is a homeomorphism of $\mathbb{R}^N$ onto the ball $B_a \subset \mathbb{R}^N$, or a homeomorphism of the ball $B_{a} \subset \mathbb{R}^N$ onto $\mathbb{R}^N$, are considered when $F(n,u)$ is periodic in the $u_j$. The approach is variational.
Citation: Jean Mawhin. Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1065-1076. doi: 10.3934/dcdss.2013.6.1065
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