There are over 100 recent articles in the literature dealing with first-, second- and third-order differential superordinations, containments and inequalities in the complex plane, none of which deals with systems of such topics. This article investigates systems of two second-order simultaneous differential containments, superordinations and inequalities in two analytic functions p and q defined in the unit disk $\mathbf{U}$. If ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$ are domains in the complex plane, then a typical example of a system of differential containments is $\begin{array}{rl}& {\mathrm{\Omega }}_1\subset \{3p\left(z\right)+z{p}^{\prime }\left(z\right)+z^2{p}^{″}\left(z\right)-q\left(z\right):z\in \mathbf{U}\},\\ & {\mathrm{\Omega }}_2\subset \{e^{z}p\left(z\right)+7z{q}^{\prime }\left(z\right)+2z^2{q}^{″}\left(z\right):z\in \mathbf{U}\}.\end{array}$ The authors determine properties of the functions p and q satisfying a variety of such systems of differential containments, superordinations and inequalities.

文献中最近有 100 多篇文章涉及复平面中的一阶、二阶和三阶微分上位、包含和不等式，但没有一篇涉及此类主题的系统。本文研究了单位盘中定义的两个解析函数p和q中的两个二阶同时微分包含、上级和不等式的系统$\mathbf{ü}$. 如果${\mathrm{\Omega }}_1$和${\mathrm{\Omega }}_2$是复平面中的域，则差分包含系统的典型示例是$\begin{array}{rl}& {\mathrm{\Omega }}_1\subset \{3p\left(z\right)+z{p}^{\text{'}}\left(z\right)+z^2{p}^{”}\left(z\right)-q\left(z\right)：z\in \mathbf{ü}\},\\ & {\mathrm{\Omega }}_2\subset \{e^{z}p\left(z\right)+7z{q}^{\text{'}}\left(z\right)+2z^2{q}^{”}\left(z\right)：z\in \mathbf{ü}\}.\end{array}$作者确定了函数p和q的性质，它们满足了各种不同的包含、上级和不等式的系统。