In this paper, we study first order interval-valued differential equations with the boundary value condition $x\left(0\right)=\alpha x\left(T\right)$. By constructing proper operators, some sufficient conditions for the existence of solutions are provided for $\alpha \in \mathbb{R}⧹\{0,1\}$, corresponding to non-periodic boundary value problems. At the end of this paper, some examples are shown to illustrate the theorems proved.

中文翻译：

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gH-可微性下区间值微分方程边值问题解的存在性

本文研究带边值条件的一阶区间值微分方程 $X（0）=\alpha X（Ť）$。通过构造适当的运算符，可以为存在解提供一些充分条件$\alpha \in \mathbb{[R}⧹\{0，\mathrm{1个}\}$，对应于非周期边值问题。在本文的最后，显示了一些例子来说明证明的定理。