On first-order differential operators with Bohr-Neugebauer type property

Aribindi Satyanarayan Rao

International Journal of Mathematics and Mathematical Sciences, 1989, vol. 12, 1-4

Abstract:

We consider a differential equation d dt u(t)-Bu(t)=f(t), where the functions u and f map the real line into a Banach space X and B: X → X is a bounded linear operator. Assuming that any Stepanov-bounded solution u is Stepanov almost-periodic when f is Bochner almost-periodic, we establish that any Stepanov-bounded solution u is Bochner almost-periodic when f is Stepanov almost-periodic. Some examples are given in which the operator d dt -B is shown to satisfy our assumption.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:703279

DOI: 10.1155/S0161171289000608

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