# American Institute of Mathematical Sciences

May  2008, 9(3&4, May): 763-785. doi: 10.3934/dcdsb.2008.9.763

## Kernel sections for processes and nonautonomous lattice systems

 1 Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NF A1C 5S7 2 Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234

Received  October 2006 Revised  January 2007 Published  February 2008

In this paper, we first establish a set of sufficient and necessaryconditions for the existence of globally attractive kernel sectionsfor processes defined on a general Banach space and a weighted spaceℓ$_\rho ^p$ of infinite sequences ($p\geq 1)$, respectively.Then we obtain an upper bound of the Kolmogorov$\varepsilon$-entropy of kernel sections for processes on theHilbert space ℓ$_\rho ^2$. As applications, we investigatecompact kernel sections for first order, partly dissipative, andsecond order nonautonomous lattice systems on weighted spacescontaining bounded sequences.
Citation: Xiao-Qiang Zhao, Shengfan Zhou. Kernel sections for processes and nonautonomous lattice systems. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 763-785. doi: 10.3934/dcdsb.2008.9.763
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