In:
International Journal of Mathematics and Mathematical Sciences, Hindawi Limited, Vol. 2004, No. 72 ( 2004), p. 3959-3964
Abstract:
We study strong solutions u : ℝ → X , a Banach space X , of the n th-order evolution equation u ( n ) − A u ( 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 ) .
Type of Medium:
Online Resource
ISSN:
0161-1712
,
1687-0425
DOI:
10.1155/S0161171204306277
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2004
detail.hit.zdb_id:
1492203-4
SSG:
17,1
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