Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy
The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated ℒp spaces, with p∈(1,∞], is admissible for a given evolution process, then this process is a nonuniform (μ,ν) contractio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/741696 |
| Summary: | The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated ℒp spaces, with p∈(1,∞], is admissible for a given evolution process, then this process is a nonuniform (μ,ν) contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform (μ,ν) contraction
and dichotomy is provided. |
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| ISSN: | 1085-3375 1687-0409 |