Electron. J. Diff. Eqns., Vol. 1998(1998), No. 33, pp. 1-11.

Instability of discrete systems

Raul Naulin & Carmen J. Vanegas

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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