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Stability sets for partial difference equations with permanent perturbation. (Spanish. English summary) Zbl 0565.39006

Differential equations and applications, Proc. 7th Congr., Granada/Spain 1984, 105-110 (1985).
[For the entire collection see Zbl 0552.00006.]
The paper is a continuation of the previous papers by the author [Actas IV C.E.D.Y.A. Sevilla, 223-229 (1981), and Actas IX Jornadas Luso- Espanolas Vol. 1, 417-420 (1982)]. The paper deals with the stability of sets for difference equations of two discrete independent variables of the form \(y(n+1,m+1)=f(n,m,y(n,m))+\Omega (n,m,y)\), n,m\(\in J\) where J is the set of integers, K - the set of real or complex numbers, H - an open subset of \(K^ q\), \(f: J^ 2\times H\to K^ q\). Applying the method of J. L. Massera [Ann. Math., II. Ser. 64, 182-206 (1956; Zbl 0070.310)] and A. Halanay [Arch. Rat. Mech. Anal. 12, 150-154 (1963; Zbl 0113.074)] the author shows, under some additional (Lipschitz) conditions on f, that if a closed subset \(G\subset H\) is uniformly asymptotically stable then it is relatively stable to permanent perturbations.
Reviewer: J.Popenda

MSC:

39A11 Stability of difference equations (MSC2000)