In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups in Hilbert spaces. Initially, we prove the existence of mild solutions by using Hausdorff measures of noncompactness and the Mönch fixed point theorem. Then, we explore the stability with continuous dependence of initial conditions, Hyers–Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, an example is given to illustrate the abstract results obtained in this paper.

中文翻译：

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具有非紧半群的随机脉冲随机偏微分方程温和解的存在性和稳定性结果

在本文中，我们研究了 Hilbert 空间中具有非紧半群的随机脉冲随机偏微分方程的温和解的存在性和一些稳定性结果。最初，我们使用 Hausdorff 非紧性测度和 Mönch 不动点定理证明了温和解的存在性。然后，我们通过开发一些新的分析技术并建立改进的不等式来探索系统的初始条件连续依赖性、Hyers-Ulam 稳定性和均方稳定性。最后给出一个例子来说明本文得到的抽象结果。