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A counter-example in the theory of almost periodic differential equations. (English) Zbl 0833.34041

It is known that if \(a(t)\) is a piecewise continuous periodic function, then any bounded solution of \(x''+ a(t) x= 0\) is almost periodic using Floquet theory. Is it still true if \(a(t)\) is merely almost periodic? The authors show by means of a counterexample to the statement that boundedness of a solution by itself implies almost periodicity. The result is also extended to linear differential equations of order \(k\).
Reviewer: P.Smith (Keele)

MSC:

34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
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References:

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