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June  2015, 20(4): 1213-1230. doi: 10.3934/dcdsb.2015.20.1213

## Pullback attractors for a class of nonlinear lattices with delays

 1 School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China, China

Received  January 2014 Revised  December 2014 Published  February 2015

We consider a class of nonlinear delay lattices $$\ddot{u}_i(t)+(-1)^p\triangle^pu_i(t)+\lambda u_i(t)+\dot{u}_i(t)=h_i(u_i(t-\rho(t)))+f_i(t),~~~i \in \mathbb{Z},$$ where $\lambda$ is a real positive constant, $p$ is any positive integer and $\triangle$ is the discrete one-dimensional Laplace operator. Under suitable conditions on $h$ and $f$ we prove the existence of pullback attractors for the multi-valued process associated with the system for which the uniqueness of solutions need not hold.
Citation: Yejuan Wang, Kuang Bai. Pullback attractors for a class of nonlinear lattices with delays. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1213-1230. doi: 10.3934/dcdsb.2015.20.1213
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