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

DOI:
https://doi.org/10.1090/S0002-9939-1981-0609651-0

MathSciNet review:
609651

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Abstract: We construct a scalar, first order, almost periodic 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