The first part of the paper is devoted to studying the continuous dependence of the solutions of Carathéodory constant delay differential equations where the vector fields satisfy classical cooperative conditions. As a consequence, when the set of considered vector fields is invariant with respect to the time-translation map, the continuity of the respective induced skew-product semiflows is obtained. These results are important for the study of the long-term behavior of the trajectories. In particular, the construction of semicontinuous semiequilibria and equilibria is extended to the context of ordinary and delay Carathéodory differential equations. Under appropriate assumptions of sublinearity, the existence of a unique continuous equilibrium, whose graph coincides with the pullback attractor for the evolution processes, is shown. The conditions under which such a solution is the forward attractor of the considered problem are outlined. Two examples of application of the developed tools are also provided.

本文的第一部分致力于研究矢量场满足经典协作条件的Carathéodory常时滞微分方程解的连续依赖性。结果，当所考虑的矢量场的集合相对于时间平移图是不变的时，获得了各个诱导的偏积半流的连续性。这些结果对于研究轨迹的长期行为很重要。特别是，将半连续半平衡和平衡的构造扩展到常和时滞Carathéodory微分方程的上下文。在亚线性的适当假设下，存在唯一连续平衡的存在，其图与演化过程的拉回吸引子重合。概述了这种解决方案是所考虑问题的吸引者的条件。还提供了两个开发工具的应用示例。