Abstract
In this paper, we study the following linear differential system
where t ↦ A(t) is a matrix valued almost periodic function. We prove that if all the solutions of the above system are almost periodic, there exists an almost periodic function b : R → Rn such that the following differential equation
has no bounded solution.
In particular, if for each almost periodic function b there exists a bounded solution to (2), there exists at least one solution for (1) that is not almost periodic.
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(Communicated by Jozef Džurina )
Acknowledgement
The authors would like to thank the anonymous referees for their useful comments that helped to improve the paper.
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