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<p>We establish a sufficient condition for the existence of a nonuniform exponential dichotomy of an evolution family on the half-line in terms of evolution semigroups. Such endeavour is not at all of a formal type and our proof is new even in the particular case of uniform exponential dichotomy.</p>

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Nonuniform Exponential Dichotomy on the Half-Line via Evolution Semigroups

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  • 出版模式：

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  • 发表日期：

    2025年2月27日

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  • Nicolae Lupa,
  • Liviu H. Popescu

摘要

We establish a sufficient condition for the existence of a nonuniform exponential dichotomy of an evolution family on the half-line in terms of evolution semigroups. Such endeavour is not at all of a formal type and our proof is new even in the particular case of uniform exponential dichotomy.