Dynamic bifurcation of nonautonomous evolution equations under Landesman–Lazer condition with cohomology methods

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-10-05 DOI:10.1016/j.nonrwa.2024.104228

Chunqiu Li, Jintao Wang

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Abstract

In this article we study the dynamic bifurcation of nonautonomous evolution equations by using cohomology methods. First, we construct a homotopy equivalence relation between the nonautonomous system and a product flow. Then, we slightly extend some continuation theorems on bifurcations for autonomous equations, and prove some new cohomology consequences on the reduced singular groups. Based on this homotopy equivalence relation and these conclusions, we establish some typical results on the dynamic bifurcation from infinity of the abstract nonautonomous evolution equation. Finally, we consider the parabolic equation

u_{t} - Δ u = λ u + f (x, u) + g (x, t)

associated with the Dirichlet boundary condition, where

f (x, u)

satisfies the appropriate Landesman–Lazer type condition. Some new results on the dynamical behaviors of this equation near resonance of the equation are derived.

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兰德斯曼-拉泽尔条件下非自治演化方程的动态分岔与同调方法

本文利用同调方法研究了非自治演化方程的动态分岔。首先，我们构建了非自治系统与乘积流之间的同调等价关系。然后，我们略微扩展了一些关于自主方程分岔的延续定理，并证明了一些关于还原奇异群的新同调后果。基于这种同调等价关系和这些结论，我们建立了抽象非自治演化方程的无穷动态分岔的一些典型结果。最后，我们考虑了与迪里夏特边界条件相关的抛物方程 ut-Δu=λu+f(x,u)+g(x,t) ，其中 f(x,u) 满足适当的 Landesman-Lazer 类型条件。推导出了该方程在共振附近的动力学行为的一些新结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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