We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg–Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

中文翻译：

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关于具有非密集定义算子的积分-微分包含的脉冲柯西问题的可解性

我们证明了对于具有非密集定义算子的 Banach 空间中的积分微分包含的脉冲柯西问题的至少一个集成解决方案的存在。由于我们寻找集成解决方案，我们不需要假设 A 是 Hille Yosida 算子。我们利用一种基于弱非紧致性度量的技术，这使我们能够避免线性部分生成的半群和非线性项上的任何紧致性假设。作为证明我们存在结果的主要工具，我们在一个固定点上使用 Glicksberg-Ky Fan 定理，用于局部凸拓扑向量空间的紧凑凸子集上的多值映射。本文是主题问题“微分和差分方程中的拓扑度和不动点理论”的一部分。