L-shadowing lemma for the Cauchy equation
Abstract
We prove that if the Cauchy problem u=Au in a Banach space is hyperbolic, then the problem has the L-shadowing property. Conversely, if the space is finite-dimensional and the L-shadowing property is satisfied, then the problem is hyperbolic. This generalizes a previous result by Ombach o, o1 for linear homeomorphisms. Some short applications are given.
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