Barbashin type characterizations for nonuniform <i>h</i>-dichotomy of evolution families

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<abstract> <p>The aim of this paper is to give some Barbashin type characterizations for the nonuniform <italic>h</italic>-dichotomy of reversible evolution families in Banach spaces. Two necessary and sufficient conditions for the nonuniform <italic>h</italic>-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.</p> </abstract>