# American Institute of Mathematical Sciences

November  2008, 21(4): 1259-1277. doi: 10.3934/dcds.2008.21.1259

## Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems

 1 Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234 2 Institute of Nonlinear Analysis, Department of Mathematics and Information Science, Wenzhou University, Zhejiang, Wenzhou 325035, China 3 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000

Received  June 2007 Revised  April 2008 Published  May 2008

In this paper, we first establish a criteria for finite fractal dimensionality of a family of compact subsets of a Hilbert space, and apply it to obtain an upper bound of fractal dimension of compact kernel sections to first order non-autonomous lattice systems. Then we consider the upper semicontinuity of kernel sections of general first order non-autonomous lattice systems and give an application.
Citation: Shengfan Zhou, Caidi Zhao, Yejuan Wang. Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1259-1277. doi: 10.3934/dcds.2008.21.1259
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