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.
"New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces." Abstr. Appl. Anal. 2016 1 - 7, 2016. https://doi.org/10.1155/2016/5098086