Monotonicity in Half-spaces for p-Laplace Problems with a Sublinear Nonlinearity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.1007/s11118-024-10157-1

Phuong Le

引用次数: 0

Abstract

We prove the monotonicity of positive solutions to the equation \(-\Delta _p u = f(u)\) in \(\mathbb {R}^N_+\) with zero Dirichlet boundary condition, where \(1<p<2\) and \(f:[0,+\infty )\rightarrow \mathbb {R}\) is a continuous function which is positive and locally Lipschitz continuous in \((0,+\infty )\) and \(\liminf _{t\rightarrow 0^+}\frac{f(t)}{t^{p-1}}>0\). Furthermore, we allow f to be sign-changing in the case \(\frac{2N+2}{N+2}<p<2\). The celebrated moving plane method will be used in the proofs of our results.

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具有亚线性非线性的 p-Laplace 问题的半空间单调性

我们证明了方程 \(-\Delta _p u = f(u)\)的正解的单调性，其中 \(1<p<2\) 和 \(f. [0,+\infty )\rightarrow \mathbb {R}^N_+\) 是在（(0,+\infty )）中正且局部 Lipschitz 连续的连续函数：((0,+\infty)\rightarrow\mathbb{R}\)是一个连续函数，在\((0,+\infty)\)和\(\liminf _{t\rightarrow 0^+}\frac{f(t)}{t^{p-1}}>0\)中是正的和局部利普希兹连续的。此外，在 \(\frac{2N+2}{N+2}<p<2\) 的情况下，我们允许 f 是符号变化的。我们将用著名的移动平面法来证明我们的结果。

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.