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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/741696 |
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| author | Yongxin Jiang Fang-fang Liao |
| author_facet | Yongxin Jiang Fang-fang Liao |
| author_sort | Yongxin Jiang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5c550cac76b644aa9d603cb7e6561b5f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5c550cac76b644aa9d603cb7e6561b5f2025-02-03T05:48:09ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/741696741696Admissibility for Nonuniform (μ,ν) Contraction and DichotomyYongxin Jiang0Fang-fang Liao1Department of Mathematics, College of Science, Hohai University, Nanjing, Jiangsu 210098, ChinaDepartment of Mathematics, College of Science, Hohai University, Nanjing, Jiangsu 210098, ChinaThe 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.http://dx.doi.org/10.1155/2012/741696 |
| spellingShingle | Yongxin Jiang Fang-fang Liao Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy Abstract and Applied Analysis |
| title | Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy |
| title_full | Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy |
| title_fullStr | Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy |
| title_full_unstemmed | Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy |
| title_short | Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy |
| title_sort | admissibility for nonuniform μ ν contraction and dichotomy |
| url | http://dx.doi.org/10.1155/2012/741696 |
| work_keys_str_mv | AT yongxinjiang admissibilityfornonuniformmncontractionanddichotomy AT fangfangliao admissibilityfornonuniformmncontractionanddichotomy |