Electron. J. Diff. Eqns., Vol. 1998(1998), No. 33, pp. 1-11.
### Instability of discrete systems

Raul Naulin & Carmen J. Vanegas

**Abstract:**

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.
Submitted September 17, 1998. Published December 8, 1998.

Math Subject Classification: 39A11, 39A10.

Key Words: Instability, Perron's Theorem, discrete dichotomies.

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Raul Naulin

Departamento de Matematicas,
Universidad de Oriente

Cumana 6101 Apartado 285, Venezuela

e-mail: rnaulin@sucre.udo.edu.ve
Carmen J. Vanegas

Departamento de Matematicas, Universidad Simon Bolivar

Caracas, Apartado 89000, Venezuela

e-mail: cvanegas@usb.ve

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