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New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces

Abstract and Applied Analysis, ISSN: 1687-0409, Vol: 2016, Page: 1-7
2016
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Article Description

We study the local exponential stability of evolution difference systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in infinite-dimensional Banach spaces, in the sense that the exponential stability for a given pseudolinear equation persists under sufficiently small perturbations. The main methodology is based on a combined use of new norm estimates for operator-valued functions with the "freezing" method.

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