发表机构
Wenzhou University（温州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用全局不变流形与Conley指标约化奇异上同调方法，研究非自治演化方程从无穷远出发的动态分支，并在Landesman-Lazer条件下证明非自治抛物方程分支新结果，改进已有工作。
AI 中文摘要
本文中，我们采用与文献中不同的全局不变流形和约化奇异上同调群方法，通过应用Conley指标理论（归功于Rybakowski），以不变集的形式研究非自治演化方程从无穷远出发的动态分支。我们首先为抽象方程建立一个非自治全局不变流形，这使得我们能够将原始系统约化到该有限维流形上。然后，构造约化方程与一个乘积流之间的同伦。最后，通过考虑Conley指标的约化奇异上同调理论，我们建立了关于该非自治方程从无穷远出发的动态分支的主要定理。作为例子，我们考虑无界域上的非自治抛物方程。在适当的Landesman-Lazer型条件下，证明了该抛物方程从无穷远出发的分支的一些新的详细结果，包括非自治Morse分解的存在性，并改进了文献中的早期工作。
英文摘要
In this paper, we use the global invariant manifold and the reduced singular cohomology groups method, which is different from those in the literature, to study the dynamic bifurcation from infinity of the nonautonomous evolution equation in terms of invariant sets by applying the Conley index theory (due to Rybakowski). We first establish a nonautonomous global invariant manifold for the abstract equation, which allows us to reduce the original system to this finite-dimensional manifold. Then, a homotopy between the reduced equation and a product flow is constructed. Finally, by considering the reduced singular cohomology theory of the Conley index, we establish our main theorems on dynamic bifurcations from infinity for this nonautonomous equation. As an example, a nonautonomous parabolic equation on unbounded domains is considered. Some new detailed results on bifurcations from infinity of the parabolic equation under an appropriate Landesman-Lazer type condition are proved, including the existence of a nonautonomous Morse decomposition, and improving the earlier works in the literature.
