Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 33, pp. 1-11.
Title: Instability of discrete systems
Authors: Raul Naulin (Univ. de Oriente, Cumana, Venezuela)
Carmen J. Vanegas (Univ. Simon Bolivar, Caracas, Venzuela)
Abstract:
In this paper, we give criteria for instability and asymptotic instability
for the null solution to the non-autonomous system of difference equations
$$ y(t+1)=A(t)y(t) + f(t,y(t)),\quad f(t,0)=0\,, $$
when the system $x(t+1)=A(t)x(t)$ 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.