Shadowing for nonautonomous difference equations with infinite delay. (October 2021)

• Record Type: Journal Article
• Authors: Dragičević, Davor; Pituk, Mihály
• Is Part Of: Applied mathematics letters. Volume 120(2021)
• Publication Date: 2021-10
• Subjects: Shadowing -- Hyers–Ulam stability -- Delay difference equation -- Infinite delay; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107284
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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. Highlights: The Hyers–Ulam stability of difference equations with infinite delay is studied. The linear part has an exponential dichotomy and the nonlinear perturbation is small. A shifted exponential dichotomy implies an exponentially weighted shadowing property.