Unstable Properties of Difference Equations

• Licet Lezama Departamento de Matemáticas, Universidad de Oriente
• Raúl Naulin Departamento de Matemáticas, Universidad de Oriente

Abstract

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