Normalized solution to p-Kirchhoff-type equation in $\mathbb {R}^{N}$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-31 DOI:10.1007/s13324-024-00954-7

ZhiMin Ren, YongYi Lan

引用次数: 0

Abstract

The paper is concerned with the p-Kirchhoff equation

$$\begin{aligned} -\left( a+b\int _{\mathbb {R}^{N}}|\nabla u|^{p}dx\right) \Delta _{p} u=f(u)-\mu u-V(x)u^{p-1}~~~~~in~~H^{1}(\mathbb {R}^{N}), \end{aligned}$$

(1)

where $a,b>0$. When $V(x)=0$, $p=2$ and $N\ge 3$, we obtain that any energy ground state normalized solutions of (1) has constant sign and is radially symmetric monotone with respect to some point in $\mathbb {R}^{N}$ by using some energy estimates. When $V(x)\not \equiv 0, p>\sqrt{3}+1, \frac{2}{p-2}<p\le N<2p$, under an explicit smallness assumption on V with $\lim _{|x|\rightarrow \infty }V(x)=\sup _{\mathbb {R}^{N}}V(x)$, we prove the existence of energy ground state normalized solutions of (1).

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p-Kirchhoff 型方程在 $$\mathbb {R}^{N}$$ 中的归一化解

本文关注的是 p-Kirchhoff 方程 $$\begin{aligned} -\left( a+b\int _{\mathbb {R}^{N}}|\nabla u|^{p}dx\right) \Delta _{p} u=f(u)-\mu u-V(x)u^{p-1}~~~~~in~~H^{1}(\mathbb {R}^{N})、\end{aligned}$$(1)where $a,b>；0$.当（V(x)=0）、（p=2）和（N≥3）时，通过使用一些能量估计，我们可以得到(1)的任何能量基态归一化解都具有恒定的符号，并且相对于（\mathbb {R}^{N}\) 中的某一点是径向对称单调的。当（V(x)not \equiv 0, p>\sqrt{3}+1, \frac{2}{p-2}<p\le N<；2p\), under an explicit smallness assumption on V with $\lim _{|x|\rightarrow \infty }V(x)=\sup _{\mathbb {R}^{N}}V(x)$, we prove existence of energy ground state normalized solutions of (1).

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.

Normalized solution to p-Kirchhoff-type equation in \(\mathbb {R}^{N}\)

Abstract