Ground state normalized solutions to the Kirchhoff equation with general nonlinearities: mass supercritical case

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-03 DOI:10.1186/s13660-024-03086-5

Qun Wang, Aixia Qian

引用次数: 0

Abstract

We study the following nonlinear mass supercritical Kirchhoff equation: $$ - \biggl(a+b \int _{\mathbb{R}^{N}} \vert \nabla u \vert ^{2} \biggr) \triangle u+ \mu u=f(u) \quad \text{in } {\mathbb{R}^{N}}, $$ where $a ,b,m>0$ are prescribed, and the normalized constrain $\int _{\mathbb{R}^{N}}|u|^{2}\,dx =m$ is satisfied in the case $1\leq N\leq 3$ . The nonlinearity f is more general and satisfies weak mass supercritical conditions. Under some mild assumptions, we establish the existence of ground state when $1\leq N\leq 3$ and obtain infinitely many radial solutions when $2\leq N\leq 3$ by constructing a particular bounded Palais–Smale sequence.

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具有一般非线性的基尔霍夫方程的基态归一化解：质量超临界情况

我们研究了以下非线性质量超临界基尔霍夫方程：$$ - \biggl(a+b \int _{\mathbb{R}^{N}} \vert \nabla u \vert ^{2} \biggr) \triangle u+ \mu u=f(u) \quad \text{in }。{\mathbb{R}^{N}}, $$ 其中$a,b,m>0$是规定的，并且归一化约束$\int _\mathbb{R}^{N}}|u|^{2}\,dx =m$在$1\leq N\leq 3$的情况下是满足的。非线性 f 更为一般，满足弱质量超临界条件。在一些温和的假设条件下，我们确定了当 $1\leq N\leq 3$ 时基态的存在，并通过构造一个特殊的有界 Palais-Smale 序列得到了当 $2\leq N\leq 3$ 时的无穷多个径向解。

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.