Abstract

In this work, we study the controllability of a class of stochastic integrodifferential equations with noncompact semigroups and nonlocal condition on Hilbert spaces.We suppose that the linear part admits a resolvent operator in the sense of Grimmer. Our main results are obtained by utilizing stochastic analysis theory, Kuratowski measure of noncompactness and Mönch fixed point Theorem. As a result, we obtain a generalization of a host of important results in the literature, without assuming the compactness of the resolvent operator. Finally, we provide an example to illustrate the efficiency of our results.

中文翻译：

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缺乏紧致性的非局部随机积分微分演化方程的可控性

摘要

在这项工作中，我们研究了一类具有非紧半群和非局域条件的随机积分微分方程在希尔伯特空间上的可控性。我们假设线性部分允许一个Grimmer意义上的解算子。我们的主要结果是通过利用随机分析理论、非紧性的 Kuratowski 测度和 Mönch 不动点定理获得的。因此，我们在不假设解析算子的紧凑性的情况下，获得了大量文献中重要结果的概括。最后，我们提供了一个例子来说明我们的结果的效率。