American Institute of Mathematical Sciences

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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

Shengfan Zhou 1, , Caidi Zhao 2, and  Yejuan Wang 3,

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.
Keywords: Upper semicontinuity., Kernel section, Fractal dimension, Non-autonomous lattice system.
Mathematics Subject Classification: 35B40, 37L50, 35Q5.
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, 2008, 21 (4) : 1259-1277. doi: 10.3934/dcds.2008.21.1259
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