Bifurcation from infinity and multiplicity of solutions for an elliptic system

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-01 DOI:10.1007/s11784-024-01101-2

Chunqiu Li, Guanyu Chen, Jintao Wang

引用次数: 0

Abstract

In this paper, we are concerned with the bifurcation from infinity and multiplicity of solutions of the semilinear elliptic system

$$\begin{aligned}&-\Delta u=\lambda u+f(x,u)-w,\\&-\Delta w=\kappa u-\zeta w, \end{aligned}$$

which can be considered as the stationary problem of reaction–diffusion equations. We treat this problem in the framework of dynamical systems, and deal with it via the approach of a pure dynamical nature, which is different from those in the literature. By using the Shape theory of attractors and the Poincaré–Lefschetz duality theory of Conley index, we establish some new multiplicity results of solutions of the system on bifurcations from infinity under an appropriate Landesman–Lazer type condition, improving the earlier works in the literature.

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椭圆系统的无穷分岔和解的多重性

本文关注半线性椭圆系统 $$\begin{aligned}&-\Delta u=\lambda u+f(x,u)-w,\&-\Delta w=\kappa u-\zeta w, \end{aligned}$$解的无穷分岔和多重性问题，该问题可视为反应扩散方程的静态问题。我们在动力学系统的框架下处理这个问题，并通过纯动力学性质的方法来处理它，这与文献中的方法不同。通过使用吸引子的形状理论和康利指数的波恩卡莱-勒夫谢茨对偶理论，我们建立了该系统在适当的兰德斯曼-拉泽尔类型条件下从无穷分岔解的一些新的多重性结果，改进了文献中的早期工作。

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.