On a higher-order evolution equation with a Stepanov-bounded solution

Aribindi Satyanarayan Rao

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-6

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 ) .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:256456

DOI: 10.1155/S0161171204306277

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