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Borg's criterion for almost periodic differential equations
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posted on 2023-06-08, 10:07 authored by Peter GieslPeter Giesl, Martin RasmussenBorg's criterion is used to prove the existence of an exponentially asymptotically stable periodic orbit of an autonomous differential equation and to determine its domain of attraction. In this article, this method is generalized to almost periodic differential equations. Both sufficient and necessary conditions are obtained for the existence of an exponentially stable almost periodic solution. The condition uses a Riemannian metric, and an example for the explicit construction of such a metric is presented.
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Publication status
- Published
Journal
Nonlinear Analysis: Theory, Methods and ApplicationsISSN
0362-546XPublisher
ElsevierExternal DOI
Issue
11Volume
69Page range
3722-3733Pages
12.0Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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