In this paper, we show the existence of mild solutions for a class of neutral partial integrodifferential equations with lack of compactness. The results are obtained using noncompact resolvent operators and a new fixed point theorem of Monch-Krasnosel’skii type. Our results are applied to a large variety of partial differential equations in which memory effects are considered. An example is provided at the end of the paper to illustrate the main results of this work.

中文翻译：

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新的Monch–Krasnosel'skii型不动点定理用于求解不带紧性的中性偏积分微分方程

在本文中，我们显示了一类缺乏紧性的中立型偏微分方程的温和解。使用非紧致分解算子和Monch-Krasnosel'skii型新的不动点定理获得结果。我们的结果适用于考虑记忆效应的各种偏微分方程。本文结尾处提供了一个示例，以说明这项工作的主要结果。