Translation Invariant Spaces and Asymptotic Properties of Variational Equations
We present a new perspective concerning the study of the asymptotic behavior of variational equations by employing function spaces techniques. We give a complete description of the dichotomous behaviors of the most general case of skew-product flows, without any assumption concerning the flow, the...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/539026 |
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| author | Adina Luminiţa Sasu Bogdan Sasu |
| author_facet | Adina Luminiţa Sasu Bogdan Sasu |
| author_sort | Adina Luminiţa Sasu |
| collection | DOAJ |
| description | We present a new perspective concerning the study of the asymptotic behavior of variational equations by employing function spaces techniques. We give a complete description of the dichotomous behaviors of the most general case of skew-product flows, without any assumption concerning the flow, the cocycle or
the splitting of the state space, our study being based only on the solvability of some associated control systems between certain function spaces. The main results do not only point out new necessary and sufficient conditions for the existence of uniform and exponential dichotomy of skew-product flows, but also provide a clear chart of the connections between the classes of translation invariant function spaces that play the role of the input or output classes with respect to certain control systems. Finally, we emphasize the significance of each underlying hypothesis by illustrative examples and present several interesting applications. |
| format | Article |
| id | doaj-art-6fff14911891481a85022c23c1f3bbd9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6fff14911891481a85022c23c1f3bbd92025-02-03T01:06:44ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/539026539026Translation Invariant Spaces and Asymptotic Properties of Variational EquationsAdina Luminiţa Sasu0Bogdan Sasu1Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Boulelvard 4, 300223 Timişoara, RomaniaDepartment of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Boulelvard 4, 300223 Timişoara, RomaniaWe present a new perspective concerning the study of the asymptotic behavior of variational equations by employing function spaces techniques. We give a complete description of the dichotomous behaviors of the most general case of skew-product flows, without any assumption concerning the flow, the cocycle or the splitting of the state space, our study being based only on the solvability of some associated control systems between certain function spaces. The main results do not only point out new necessary and sufficient conditions for the existence of uniform and exponential dichotomy of skew-product flows, but also provide a clear chart of the connections between the classes of translation invariant function spaces that play the role of the input or output classes with respect to certain control systems. Finally, we emphasize the significance of each underlying hypothesis by illustrative examples and present several interesting applications.http://dx.doi.org/10.1155/2011/539026 |
| spellingShingle | Adina Luminiţa Sasu Bogdan Sasu Translation Invariant Spaces and Asymptotic Properties of Variational Equations Abstract and Applied Analysis |
| title | Translation Invariant Spaces and Asymptotic Properties of Variational Equations |
| title_full | Translation Invariant Spaces and Asymptotic Properties of Variational Equations |
| title_fullStr | Translation Invariant Spaces and Asymptotic Properties of Variational Equations |
| title_full_unstemmed | Translation Invariant Spaces and Asymptotic Properties of Variational Equations |
| title_short | Translation Invariant Spaces and Asymptotic Properties of Variational Equations |
| title_sort | translation invariant spaces and asymptotic properties of variational equations |
| url | http://dx.doi.org/10.1155/2011/539026 |
| work_keys_str_mv | AT adinaluminitasasu translationinvariantspacesandasymptoticpropertiesofvariationalequations AT bogdansasu translationinvariantspacesandasymptoticpropertiesofvariationalequations |