Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 29, pp. 1-25.

Title: Construction of almost periodic functions with given properties

Author: Michal Vesely (Masaryk Univ., Brno, Czech Republic)

Abstract: 
 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.