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摘要
In this paper, we reveal the deep relation between Stepanov and piecewise continuous almost periodic functions and apply it to the study of almost periodic impulsive differential equations. Under the quasi-uniform continuity condition, the equivalence of Stepanov and piecewise continuous almost periodic functions is firstly established, which provides both a generalization of Bochner's theorem and a powerful tool to investigate piecewise continuous almost periodic functions. As applications, the module containment for piecewise continuous almost periodic solutions to linear impulsive differential equations is studied.
