hrvatski

Weighted shadowing for delay differential equations

After introducing the notion of weighted shadowing, we give sufficient conditions under which certain nonlinear perturbations of nonautonomous linear delay differential equations exhibit the shadowing property with respect to a given weight function. As a corollary, it is shown that if the unperturbed equation admits a shifted exponential dichotomy and the Lipschitz constant of the nonlinear term is sufficiently small, then the perturbed system has a shadowing property with respect to an exponential weight function. An application to differential equations with small delay is given. The results are new even in the case of the standard shadowing property.

shadowing property ; delay differential equation ; exponential dichotomy

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