On a higher-order evolution equation with a Stepanov-bounded solution
We study strong solutions u:ℝ→X, a Banach space X, of the nth-order evolution equation u(n)−Au(n−1)=f, an infinitesimal generator of a strongly continuous group A:D(A)⊆X→X, and a given forcing term f:ℝ→X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306277 |
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| _version_ | 1832558420131053568 |
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| author | Aribindi Satyanarayan Rao |
| author_facet | Aribindi Satyanarayan Rao |
| author_sort | Aribindi Satyanarayan Rao |
| collection | DOAJ |
| description | We study strong solutions u:ℝ→X, a Banach space X, of the nth-order evolution equation u(n)−Au(n−1)=f, an infinitesimal generator of a strongly continuous group A:D(A)⊆X→X, and a given forcing term f:ℝ→X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost periodic, then u and all derivatives u′,…,u(n−1) are strongly almost periodic. In the case of a general Banach space X, a corresponding result is obtained, proving weak almost periodicity of u, u′,…,u(n−1). |
| format | Article |
| id | doaj-art-e9c4ac1ec76445f8b89e3b14ca27848c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e9c4ac1ec76445f8b89e3b14ca27848c2025-02-03T01:32:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004723959396410.1155/S0161171204306277On a higher-order evolution equation with a Stepanov-bounded solutionAribindi Satyanarayan Rao0Department of Computer Science, Vanier College, 821 Avenue Ste Croix, St. Laurent H4L 3X9, Quebec, CanadaWe study strong solutions u:ℝ→X, a Banach space X, of the nth-order evolution equation u(n)−Au(n−1)=f, an infinitesimal generator of a strongly continuous group A:D(A)⊆X→X, and a given forcing term f:ℝ→X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost periodic, then u and all derivatives u′,…,u(n−1) are strongly almost periodic. In the case of a general Banach space X, a corresponding result is obtained, proving weak almost periodicity of u, u′,…,u(n−1).http://dx.doi.org/10.1155/S0161171204306277 |
| spellingShingle | Aribindi Satyanarayan Rao On a higher-order evolution equation with a Stepanov-bounded solution International Journal of Mathematics and Mathematical Sciences |
| title | On a higher-order evolution equation with a Stepanov-bounded solution |
| title_full | On a higher-order evolution equation with a Stepanov-bounded solution |
| title_fullStr | On a higher-order evolution equation with a Stepanov-bounded solution |
| title_full_unstemmed | On a higher-order evolution equation with a Stepanov-bounded solution |
| title_short | On a higher-order evolution equation with a Stepanov-bounded solution |
| title_sort | on a higher order evolution equation with a stepanov bounded solution |
| url | http://dx.doi.org/10.1155/S0161171204306277 |
| work_keys_str_mv | AT aribindisatyanarayanrao onahigherorderevolutionequationwithastepanovboundedsolution |