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Borg's criterion for almost periodic differential equations

journal contribution
posted on 2023-06-08, 10:07 authored by Peter GieslPeter Giesl, Martin Rasmussen
Borg'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.

History

Publication status

  • Published

Journal

Nonlinear Analysis: Theory, Methods and Applications

ISSN

0362-546X

Publisher

Elsevier

Issue

11

Volume

69

Page range

3722-3733

Pages

12.0

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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