On a question in the theory of almost periodic differential equations

Hu, Zuo; Mingarelli, Angelo

doi:10.1090/S0002-9939-99-04738-3

On a question in the theory of almost periodic differential equations
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by Zuo Sheng Hu and Angelo B. Mingarelli PDF

Proc. Amer. Math. Soc. 127 (1999), 2665-2670 Request permission

Abstract:

We show that there exists a real homogeneous differential equation of order $n$ with classical almost periodic coefficients such that all solutions are uniformly bounded on the real line yet no non-trivial solution is almost periodic. This now appears to make the search for a Floquet theory of such equations a futile enterprise.

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