engleski

Shadowing for nonautonomous difference equations with infinite delay

We formulate sufficient conditions under which a large class of semilinear nonautonomous difference equations with infinite delay is Hyers-Ulam stable. These conditions require that the nonautonomous linear part admits an exponential dichotomy and that the nonlinear perturbations are uniformly Lipschitz continuous with a sufficiently small Lipschitz constant. In the more general situation when the linear part admits a shifted exponential dichotomy, we are able to provide sufficient conditions for the existence of a certain weighted form of the shadowing property.

shadowing ; Hyers-Ulam stability ; delay difference equations ; infinite delay

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