Affiliation:
1. Institut für Mathematik , Universität Klagenfurt , Universitätsstraße 65–67, 9020 Klagenfurt , Austria
Abstract
Abstract
The purpose of this informal paper is three-fold: First, filling a gap in the literature, we provide a (necessary and sufficient) principle of linearized stability for nonautonomous difference equations in Banach spaces based on the dichotomy spectrum. Second, complementing the above, we survey and exemplify an ambient nonautonomous and infinite-dimensional center manifold reduction, that is Pliss’s reduction principle suitable for critical stability situations. Third, these results are applied to integrodifference equations of Hammerstein- and Urysohn-type both in C- and Lp
-spaces. Specific features of the nonautonomous case are underlined. Yet, for the simpler situation of periodic time-dependence even explicit computations are feasible.
Subject
Applied Mathematics,Numerical Analysis,Statistics and Probability,Analysis
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