Naulin, Raúl; Vanegas, Carmen J.

Instability of discrete systems

Electron. J. Differ. Equ. 1998, Paper No. 33, 11 p. (1998)

Summary

Summary: In this paper, we give criteria for instability and asymptotic instability for the null solution to the non-autonomous system of difference equations $y(t+1)=A(t)y(t) + f(t,y(t)), f(t,0)=0$, when the system $x(t+1)$=(t)$x(t)$ is unstable. In particular for A constant, we study instability from a new point of view. Our results are obtained using the method of discrete dichotomies, and cover a class of difference systems for which instability properties cannot be deduced from the classical results by Perron and Coppel.

Mathematics Subject Classification

39A11, 39A10

Keywords/Phrases

instability, Perron's theorem, discrete dichotomies

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