Abstract In this paper, we consider the non-autonomous semilinear impulsive differential equations with state-dependent delay. The approximate controllability results of the first-order systems are obtained in a separable reflexive Banach space, which has a uniformly convex dual. In order to establish sufficient conditions of the approximate controllability of such a system, we have used the theory of linear evolution systems, properties of the resolvent operator and Schauder’s fixed point theorem. Finally, we provide two concrete examples to validate our results.

中文翻译：

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Banach空间中状态依赖延迟的非自主脉冲演化方程的近似可控性

摘要 在本文中，我们考虑了具有状态相关延迟的非自治半线性脉冲微分方程。一阶系统的近似可控性结果是在具有一致凸对偶的可分离自反Banach空间中获得的。为了建立这样一个系统的近似可控性的充分条件，我们使用了线性演化系统的理论、解算符的性质和Schauder不动点定理。最后，我们提供了两个具体的例子来验证我们的结果。