Some results on the nonuniform polynomial dichotomy of discrete evolution families

Abstract

This paper studies the existence of nonuniform polynomial dichotomy for discrete evolution families in Banach spaces. Some necessary and sufficient conditions for the nonuniform polynomial dichotomy concept of discrete evolution families with respect to invariant projections sequence and strongly invariant projections sequence are obtained, respectively. Additionally, we consider two notions of Lyapunov functions and use our results to obtain the relations between (generalized) Lyapunov functions and nonuniform polynomial dichotomy.

Topics & Concepts