A Note on Almost Periodic Variational Equations
- The variational equation of a nonautonomous differential equation along a solution mu is given. We consider the question if the variational equation is almost periodic provided that the original equation is almost periodic by a discussion of the following problem: Is the derivative D_xF almost periodic whenever F is almost periodic? We give a negative answer in this paper, and the counterexample relies on an explicit construction of a scalar almost periodic function whose derivative is not almost periodic. Moreover, we provide a necessary and sufficient condition for the derivative D_xF to be almost periodic.
| Author: | Peter Giesl, Martin RasmussenORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-5071 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/639 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2008-13) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2008/03/18 |
| Tag: | Almost periodic differential equation; almost periodic function; variational equation |
| GND-Keyword: | Fastperiodische Differentialgleichung; Fastperiodische Funktion; Variationsgleichung |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
