Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 244, pp. 1-17.
Lyapunov functions for general nonuniform
trichotomy with different growth rates
Yongxin Jiang, Fang-Fang Liao
Abstract:
In this article, we consider non-autonomous linear equations x' = A(t)x
that may exhibit stable, unstable and central behaviors in different directions.
We give a complete characterization of nonuniform
trichotomies
in terms of strict Lyapunov functions. In particular, we obtain an inverse
theorem giving explicitly Lyapunov functions for each given trichotomy.
The main novelty of our work is that we consider a very general type of
nonuniform exponential trichotomy, which admits different growth rates in
the uniform and nonuniform parts.
Submitted April 12, 2014. Published November 20, 2014.
Math Subject Classifications: 34A30, 37B25.
Key Words: Lyapunov functions; autonomous systems; nonuniform trichotomies;
hyperbolicity.
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Yongxin Jiang
Department of Mathematics
College of Science, Hohai University
Nanjing 210098, China
email: yxinjiang@hhu.edu.cn, fax +86 (025) 8378-6626
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Fang-Fang Liao
Department of Mathematics
College of Science, Hohai University
Nanjing 210098, China
email: liaofangfang8178@sina.com
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