The paper introduces nonuniform exponential dichotomies, exploring their roughness and implications for asymptotic behavior.
In this paper, we introduce the concept of nonuniform ‐exponential dichotomies to formulate an asymptotic behavior weaker than the known nonuniform ‐exponential dichotomy. We discuss the roughness of such dichotomies on the whole line and the half line separately without global invertibility of the evolution family. Our results extend the known results to nonuniform ‐exponential dichotomies in the case that or .
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Chen et al. (2026) studied this question.
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