Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line

Journal article

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.

Authors: Arendt, W; Batty, C

• Publication status: Published
• Journal: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
• Volume: 31
• Issue: 3
• Pages: 291-304
• Publication date: 1999-05-01
• DOI: 10.1112/S0024609398005657
• EISSN: 1469-2120
• ISSN: 0024-6093
• Language: English