By using the Banach fixed point theorem and Schauder fixed-point theorem for semilinear spaces, we study the existence of solutions to some class of boundary value problems for interval-valued differential equations on unbounded domains. Some sufficient conditions are provided in order to deduce the existence of solutions without switching points, and also for mixed solutions with a unique switching point. The influences of the range of the parameter in the boundary value condition has on the existence of solutions is also discussed. Finally, two examples are given to demonstrate the feasibility of the theorems.

中文翻译：

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无界域上区间值微分方程的边值问题

利用半线性空间的Banach不动点定理和Schauder不动点定理，研究了无界域上区间值微分方程的一类边值问题解的存在性。提供了一些充分条件来推断没有切换点的解的存在，以及具有唯一切换点的混合解。还讨论了边值条件下参数取值范围对解存在性的影响。最后，给出了两个例子来证明定理的可行性。