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 the nonlinear perturbations are uniformly Lipschitz continuous with a sufficiently small Lipschitz constant. In the more general case 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.

中文翻译：

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具有无限延迟的非自治差分方程的遮蔽

我们制定了充分的条件，在这些条件下，一大类具有无限延迟的半线性非自治差分方程是Hyers–Ulam稳定的。这些条件要求非自治线性部分接受指数二分法，并且非线性扰动以足够小的Lipschitz常数均匀地进行Lipschitz连续。在更一般的情况下，当线性部分允许转移指数二分法时，我们能够为阴影属性的某些加权形式的存在提供足够的条件。