Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A linear, almost periodic equation with an almost automorphic solution
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by Russell A. Johnson
Proc. Amer. Math. Soc. 82 (1981), 199-205
DOI: https://doi.org/10.1090/S0002-9939-1981-0609651-0

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.
References
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Bibliographic Information
  • © Copyright 1981 American Mathematical Society
  • 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