Barbashin type characterizations for nonuniform h-dichotomy of evolution families

Abstract

The aim of this paper is to give some Barbashin type characterizations for the nonuniform h-dichotomy of reversible evolution families in Banach spaces. Two necessary and sufficient conditions for the nonuniform h-dichotomy are pointed out using some important sets of growth functions. Additionally, as particular cases, we obtain a Barbashin type characterization for nonuniform exponential dichotomy and a necessary and sufficient condition for the nonuniform polynomial dichotomy.

Keywords

• nonuniform h-dichotomy
• evolution family
• growth rate
• barbashin type theorem
• nonuniform exponential dichotomy
• nonuniform polynomial dichotomy