Nonuniform instability for evolution families

Abstract

The aim of this paper is to study the relationship between the notions of nonuniform exponential instability for evolutionary processes and admissibility of the pair of spaces (C00 ( R+, X), C(R+, X)). The evolutionary processes considered are the most general in the sense that they do not require uniform or nonuniform growth. A necessary condition for expansiveness of the evolutionary processes is given.