AI 中文总结
本文建立了泛函常微分方程的存在唯一性定理，推导了用于表征双色透镜存在性的泛函常微分方程组，证明了二维双色透镜存在并将结果推广至三维。
AI 中文摘要
本文在比现有文献更弱的假设下，建立了一类泛函常微分方程的存在性与唯一性定理。接着，我们考虑设计一种透镜，它能将点光源发出的两种不同频率的光线折射为同一准直光束。我们推导了一个泛函常微分方程组，其可解性表征了此类透镜的存在性。利用该存在性定理，我们证明了二维情形下此类透镜存在，随后将相应结果推广至三维情形。
英文摘要
This paper establishes an existence and uniqueness theorem for a class of functional ordinary differential equations under assumptions weaker than those found in the literature. We then consider the problem of designing a lens that refracts rays of two distinct frequencies emitted from a point source into a common collimated beam. We derive a system of functional ordinary differential equations whose solvability characterizes the existence of such lenses. Using the existence theorem, we prove that such a lens exists in two dimensions. We then extend the corresponding result to three dimensions.
