通过扰动策略实现仿射 p 拉普拉斯方程的非微观解

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-08 DOI:10.1016/j.nonrwa.2024.104154

Edir Júnior Ferreira Leite , Marcos Montenegro

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引用次数: 0

摘要

本文关注的是仿射 p-Laplace 方程的非微观解的存在性问题，该方程涉及亚临界非线性，在 u=0 时表现为 uq（含 q<p-1），在无穷远处表现为 ur（含 r>p-1）。由于仿射能量型函数的局部 Palais-Smale compactness 是一个未解决的难题，因此通过使用空间规范的扰动方法来解决这个问题。根据修正仿射背景下相应临界点的极限过程，构建了穿山临界点。同时还解决了 MP 解集的紧凑性和稳定性问题。

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Nontrivial solutions to affine p-Laplace equations via a perturbation strategy

This paper is concerned with the existence of nontrivial solutions for affine $p$ -Laplace equations involving subcritical nonlinearities behaving at $u = 0$ as $u^{q}$ with $q p - 1$ . Since local Palais–Smale compactness for affine energy type functionals is an open hard question, the problem is overcome by means of a perturbative approach using the space norm. Mountain-pass critical points are constructed from a limit process of corresponding ones in the modified affine context. Compactness and stability of MP solution sets are also addressed.

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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.