Abstract We give new criteria for nonuniform dichotomy of nonautonomous systems on the whole line in terms of admissibility relative to an integral equation. In our approach the input space I ( R , X ) is an intersection of spaces that can be successively minimized and the output space C ( R , X ) can be one of some well-known spaces of continuous functions. Using computational arguments, we show that the admissibility of ( C ( R , X ) , I ( R , X ) ) leads to a nonuniform exponential dichotomy. We expose a complete analysis of the connections between admissibility and nonuniform dichotomy on the whole line and we also discuss several interesting consequences. Moreover, we obtain the explicit expression of the growth rates for dichotomy in terms of the initial exponential growth and the norm of the input-output operator. Finally, we present a direct application of the main result in the case of evolution families which admit uniform exponential growth.

中文翻译：

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全线非自治系统非均匀二分行为的可接受标准

摘要 我们根据相对于积分方程的可接受性，给出了整条线上非自治系统的非均匀二分法的新标准。在我们的方法中，输入空间 I ( R , X ) 是可以连续最小化的空间的交集，输出空间 C ( R , X ) 可以是一些著名的连续函数空间之一。使用计算参数，我们表明 ( C ( R , X ) , I ( R , X ) ) 的可容许性导致非均匀指数二分法。我们对整条线上的可受理性和非均匀二分法之间的联系进行了完整的分析，我们还讨论了几个有趣的结果。此外，我们根据初始指数增长和输入-输出算子的范数获得了二分法增长率的显式表达。最后，