论文标题
单调偏斜产品半流量，用于Carathéodory微分方程和应用
Monotone skew-product semiflows for Carathéodory differential equations and applications
论文作者
论文摘要
本文的第一部分致力于研究carathéodory恒定延迟差分方程的解决方案的连续依赖性，其中矢量场满足了经典的合作条件。结果，当考虑到时间翻译图的被考虑的矢量场集合不变时，可以获得相应诱导的偏斜产物半循环的连续性。这些结果对于研究轨迹的长期行为很重要。特别是，半连续半喹啉和平衡的构建扩展到普通和延迟的carathéodory微分方程的背景。在适当的假设假设下，显示了独特的连续平衡的存在，其图与进化过程中的回缩吸引子一致。概述了这种解决方案是所考虑问题的正向吸引子的条件。还提供了两个应用工具应用的示例。
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.
