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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Hindawi Limited
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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doaj-e9c4ac1ec76445f8b89e3b14ca27848c2020-11-24T21:39:12ZengHindawi LimitedInternational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Aribindi Satyanarayan Rao |
| spellingShingle |
Aribindi Satyanarayan Rao On a higher-order evolution equation with a Stepanov-bounded solution International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Aribindi Satyanarayan Rao |
| author_sort |
Aribindi Satyanarayan Rao |
| title |
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_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_sort |
on a higher-order evolution equation with a stepanov-bounded solution |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| 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). |
| url |
http://dx.doi.org/10.1155/S0161171204306277 |
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AT aribindisatyanarayanrao onahigherorderevolutionequationwithastepanovboundedsolution |
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