In this paper, we mainly investigate properties on solution sets of a semi-linear stochastic evolution integro-differential inclusion with Poisson jumps and non-local initial conditions. We firstly establish the existence of solutions to the addressed equation via weak topology technique. Through establishing the estimate on noncompactness measure of integrals for Poisson jumps, we further show that the solution set is a compact $R_{\delta }$-set when the resolvent operator is compact or non-compact, respectively.

中文翻译：

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具有泊松跳跃和非局部初始条件的半线性随机演化积分-微分夹杂物的解

在本文中，我们主要研究了具有泊松跳跃和非局部初始条件的半线性随机演化积分-微分包含的解集的性质。我们首先通过弱拓扑技术确定所寻址方程的解的存在性。通过建立泊松跳积分的非紧性测度估计，进一步证明解集是紧的$R_{\delta }$-分别在解析运算符是紧凑或非紧凑时设置。