1. On the instability of linear nonautonomous delay systems
- Creator:
- Naulin, Raúl
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Liapounov instability, $h$-instability, instability of delay equations, and nonconstant delays
- Language:
- English
- Description:
- The unstable properties of the linear nonautonomous delay system $x^{\prime }(t)=A(t)x(t)+B(t)x(t-r(t))$, with nonconstant delay $r(t)$, are studied. It is assumed that the linear system $y^{\prime }(t)=(A(t)+B(t))y(t)$ is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay $r(t)$ is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function $r(t)$ and the results depending on the asymptotic properties of the delay function.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public