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

Aribindi Satyanarayan Rao
1989 International Journal of Mathematics and Mathematical Sciences  
We consider a differential equationddtu(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 operatorddt-B is shown to satisfy our assumption.
doi:10.1155/s0161171289000608 fatcat:ojcpfjxxprekxjh3r4lfu5cbku