格点系统存在指数吸引子的充分条件及应用

Sufficient Conditions for the Existence of Exponential Attractors for Lattice Systems and Applications

本文给出了一般格点动力系统存在指数吸引子的充分条件,然后将得到的结果应用到下面的格点非线性Schr(o|¨)dinger方程:iu_m-γ(2u_m-u_(m+1)-u_(m-1))+iκu_m+δ|u_m|^(2σ)u_m=g_m,m∈Z.设γ,κ,δ,σ和g_m满足适当的条件,证明了该格点方程存在指数吸引子.

We first recast some sufficient conditions for the existence of exponential attractors for general lattice dynamical systems. Then we apply the result to the following nonlinear SchrSdinger equations on infinite lattices：ium-γ（2um-um＋1-um-1）＋ikum＋δ｜um｜^2σum=gm,m∈Z. Under some conditions on γ,κ,δ,σ and gm the existence of exponential attractors is established.