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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A linear, almost periodic equation with an almost automorphic solution


Author: Russell A. Johnson
Journal: Proc. Amer. Math. Soc. 82 (1981), 199-205
MSC: Primary 34C28; Secondary 54H20
MathSciNet review: 609651
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Abstract: We construct a scalar, first order, almost periodic $ {\text{ODE}}( * )x + A(t)x = B(t)$ which admits bounded solutions, but no almost periodic solutions. Using this equation, we give an example of a two-dimensional, almost periodic system whose projective flow admits two minimal subsets, one of which is almost automorphic but not almost periodic. Finally, we show that some equation in the hull of $ ( * )$ admits an almost automorphic, nonalmost periodic solution.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0609651-0
Article copyright: © Copyright 1981 American Mathematical Society