Electron. J. Diff. Equ., Vol. 2011 (2011), No. 29, pp. 1-25.

Construction of almost periodic functions with given properties

Michal Vesely

We define almost periodic functions with values in a pseudometric space $\mathcal{X}$. We mention the Bohr and the Bochner definition of almost periodicity. We present one modifiable method for constructing almost periodic functions in $\mathcal{X}$. Applying this method, we prove that in any neighbourhood of an almost periodic skew-Hermitian linear differential system there exists a system which does not possess a nontrivial almost periodic solution.

Submitted August 22, 2010. Published February 18, 2011.
Math Subject Classifications: 34A30, 34C27, 42A75.
Key Words: Almost periodic solutions; linear differential equations; skew-Hermitian systems.

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Michal Vesely
Department of Mathematics and Statistics
Masaryk University
Kotlarska 2, CZ-611 37 Brno, Czech Republic
email: michal.vesely@mail.muni.cz

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