Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line
Let u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: u′(t) = Au(t) + (Latin small letter o with stroke)(t) (t ≥ 0). Suppose that u has uniformly convergent means, σ(A) ∩ i R is countable, and (Latin small letter o with stroke) is asymptotically almost per...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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1999
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| _version_ | 1797053173257469952 |
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| author | Arendt, W Batty, C |
| author_facet | Arendt, W Batty, C |
| author_sort | Arendt, W |
| collection | OXFORD |
| description | Let u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: u′(t) = Au(t) + (Latin small letter o with stroke)(t) (t ≥ 0). Suppose that u has uniformly convergent means, σ(A) ∩ i R is countable, and (Latin small letter o with stroke) is asymptotically almost periodic. Then u asymptotically almost periodic. Related results have been obtained by Ruess and Vũ, and by Basit, using different methods. A direct proof is given of a Tauberian theorem of Batty, van Neerven and Räbiger, and applications to Volterra equations are discussed. |
| first_indexed | 2024-03-06T18:40:17Z |
| format | Journal article |
| id | oxford-uuid:0ca47293-e973-4368-a154-710e81562195 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:40:17Z |
| publishDate | 1999 |
| record_format | dspace |
| spelling | oxford-uuid:0ca47293-e973-4368-a154-710e815621952022-03-26T09:36:07ZAsymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-lineJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0ca47293-e973-4368-a154-710e81562195EnglishSymplectic Elements at Oxford1999Arendt, WBatty, CLet u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: u′(t) = Au(t) + (Latin small letter o with stroke)(t) (t ≥ 0). Suppose that u has uniformly convergent means, σ(A) ∩ i R is countable, and (Latin small letter o with stroke) is asymptotically almost periodic. Then u asymptotically almost periodic. Related results have been obtained by Ruess and Vũ, and by Basit, using different methods. A direct proof is given of a Tauberian theorem of Batty, van Neerven and Räbiger, and applications to Volterra equations are discussed. |
| spellingShingle | Arendt, W Batty, C Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line |
| title | Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line |
| title_full | Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line |
| title_fullStr | Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line |
| title_full_unstemmed | Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line |
| title_short | Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line |
| title_sort | asymptotically almost periodic solutions of inhomogeneous cauchy problems on the half line |
| work_keys_str_mv | AT arendtw asymptoticallyalmostperiodicsolutionsofinhomogeneouscauchyproblemsonthehalfline AT battyc asymptoticallyalmostperiodicsolutionsofinhomogeneouscauchyproblemsonthehalfline |