On first-order differential operators with Bohr-Neugebauer type property
We consider a differential equation ddtu(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 Ste...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000608 |
| Summary: | We consider a differential equation ddtu(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 ddt-B is shown to satisfy our assumption. |
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| ISSN: | 0161-1712 1687-0425 |