Pullback attractors  for a class of nonlinear  lattices with delays

Yejuan Wang; Kuang Bai

doi:10.3934/dcdsb.2015.20.1213

Article Contents

2015, Volume 20, Issue 4: 1213-1230. Doi: 10.3934/dcdsb.2015.20.1213

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Pullback attractors for a class of nonlinear lattices with delays

Yejuan Wang^1, and
Kuang Bai^1,

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

Received: December 31, 2013

Revised: November 30, 2014

Published: May 2015

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Abstract

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.

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Mathematics Subject Classification: 34K05, 34K31, 35B40, 35B41, 35L05.

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References

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