Unstable Properties of Difference Equations - Lezama, Licet; Naulin, Raúl (Ciencia, 1970)
In this paper two theorems on instability and asymptotic instability for the null solution of the nonautonomous system of difference equations x(n+1) = A(n)x(n) + f(n,x(n)), f(n,0) = 0, are proven. The main hypotheses are the existence of an (1,k)-dichotomy for the linear system y(n+1) = A(n)y(n) and a monotone condition for f(n,x). The obtained results cover a class of difference systems, which unstable properties cannot be deduced from the classical results on instability of Perron and Coppel