A note on amost periodic variational equations

Giesl, Peter and Rasmussen, Martin (2011) A note on amost periodic variational equations. Communications on Pure and Applied Analysis, 10 (3). pp. 983-994. ISSN 1534-0392

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The variational equation of a nonautonomous differential equation (x) over dot = F(t, x) along a solution mu is given by (x) over dot = DxF(t, mu(t))x. We consider the question whether the variational equation is almost periodic provided that the original equation is almost periodic by a discussion of the following problem: Is the derivative DxF 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 DxF to be almost periodic.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 19:33
Last Modified: 12 Jun 2012 12:41
URI: http://sro.sussex.ac.uk/id/eprint/21263
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