This article presents a survey of several properties of the set of solutions for a differential inclusion involving a time-delayed component and with right-hand side parametrized by either an upper semicontinuous or lower semicontinuous multifunction. Our results include: existence of solutions, compactness and contractibility of the solution and reachable sets in the upper semicontinuous case, precompactness and connectedness of the solution and reachable sets in the lower semicontinuous case, regularity of the solution and reachable mappings with respect to parameters, and existence of solutions for a dynamic optimization problem.

中文翻译：

---

时滞不连续动力学解集的定性性质

本文介绍了一组微分包含问题的解决方案的一些性质，其中包括一个时滞分量，并且右侧参数由上半连续或下半连续多功能参数化。我们的结果包括：解的存在，在上半连续情况下解决方案和可及集的紧致性和可收缩性，在下半​​连续情况下解决方案与可联系集的预紧性和连通性，解的规则性和参数的可及映射以及动态优化问题解决方案的存在。