Properties of fractional p-Laplace equations with sign-changing potential

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-09 DOI:10.1016/j.na.2024.113628

Yubo Duan , Yawei Wei

引用次数: 0

Abstract

In this paper, we consider the nonlinear equation involving the fractional p-Laplacian with sign-changing potential. This model draws inspiration from De Giorgi Conjecture. There are two main results in this paper. Firstly, we obtain that the solution is radially symmetric within the bounded domain, by applying the moving plane method. Secondly, by exploiting the idea of the sliding method, we construct the appropriate auxiliary functions to prove that the solution is monotone increasing in some direction in the unbounded domain. The different properties of the solution in bounded and unbounded domains are mainly attributed to the inherent non-locality of the fractional p-Laplacian.

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符号变化势分数 p 拉普拉斯方程的性质

在本文中，我们考虑了涉及符号变化势的分数 p-拉普拉奇的非线性方程。这一模型的灵感来自 De Giorgi 猜想。本文有两个主要结果。首先，我们通过应用移动平面法，得到了解在有界域内是径向对称的。其次，利用滑动法的思想，我们构造了适当的辅助函数，证明解在无界域中的某个方向上是单调递增的。有界域和无界域解的不同性质主要归因于分数 p-Laplacian 固有的非位置性。

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.