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.