The aim of this work is to investigate the existence and uniqueness of μ-pseudo almost periodic (resp. μ-pseudo compact almost automorphic) weak solutions for the following partial functional differential inclusion: $x^{\mathrm{\prime }}\left(t\right)+\mathcal{A}x\left(t\right)\ni f(t,x_t)\mathrm{f}\mathrm{o}\mathrm{r}t\in \mathbb{R},$where $\mathcal{A}:\mathcal{H}⟶2^{\mathcal{H}}$ is a strongly maximal monotone operator on a real Hilbert space $\mathcal{H}$, $f:\mathbb{R}\times \mathcal{C}⟶\mathcal{H}$ is a Stepanov μ-pseudo almost periodic (resp. μ-pseudo compact almost automorphic) function of class r, $\mathcal{C}=C\left(\right[-r,0],\mathcal{H})$ is the Banach space of all continuous functions from $[-r,0]$ to $\mathcal{H}$ and the history function $x_t$ is defined by $x_t\left(\theta \right)=x(t+\theta )$ for $\theta \in [-r,0]$. Two examples are given for parabolic and subdifferential systems.

这项工作的目的是研究以下偏泛函微分包含的 μ -伪几乎周期性（resp. μ -伪紧几乎自守）弱解的存在性和唯一性：$X^{\mathrm{\text{'}}}\left(吨\right)+\mathcal{一个}X\left(吨\right)\ni F(吨,X_{吨})\mathrm{F}\mathrm{○}\mathrm{r}吨\in \mathbb{R},$在哪里$\mathcal{一个}：\mathcal{H}⟶2^{\mathcal{H}}$是实希尔伯特空间上的强极大单调算子$\mathcal{H}$,$F：\mathbb{R}\times \mathcal{C}⟶\mathcal{H}$是类r的 Stepanov μ -pseudo 几乎周期性（resp. μ -pseudo compact 几乎自守）函数，$\mathcal{C}=C\left(\right[-r,0],\mathcal{H})$是所有连续函数的 Banach 空间$[-r,0]$至$\mathcal{H}$和历史函数$X_{吨}$定义为$X_{吨}\left(\theta \right)=X(吨+\theta )$为了$\theta \in [-r,0]$. 给出了抛物线和次微分系统的两个例子。