Non-Degeneracy and Infinitely Many Solutions for Critical SchrÖDinger-Maxwell Type Problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-25 DOI:10.1007/s11118-024-10123-x

Yuxia Guo, Yichen Hu, Shaolong Peng

引用次数: 0

Abstract

In this paper, we consider the following Schrödinger-Maxwell type equation with critical exponent \(-\Delta u=K(y)\Big (\frac{1}{|x|^{n-2}}*K(x)|u|^{\frac{n+2}{n-2}}\Big )u^{\frac{4}{n-2}},\quad {in}\,\, \mathbb {R}^n, \qquad \text {(0.1)}\) where the function K satisfies the assumption \(\mathcal {F}\), and \(*\) stands for the standard convolution. We first derived the non-degeneracy result for the critical Schrödinger-Maxwell equation. Then, as an application, we proved that problem Eq. (0.1) admits infinitely many non-radial positive solutions with arbitrary large energy. We believe that the various new ideas and technique computations that we used in this paper would be useful to deal with other related elliptic problems involving convolution nonlinear terms.

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临界薛定谔-麦克斯韦式问题的非退行性和无限多解

在本文中，我们考虑以下具有临界指数的薛定谔-麦克斯韦式方程（-/Delta u=K(y)\Big (\frac{1}{|x|^{n-2}}*K(x)|u|^{frac{n+2}{n-2}}\Big )u^{frac{4}{n-2}}、\quad {in}\,\mathbb {R}^n, \qquad \text {(0.1)}），其中函数 K 满足假设（\(\mathcal {F}\），而\(*\)代表标准卷积。我们首先得出了临界薛定谔-麦克斯韦方程的非退化结果。然后，作为一个应用，我们证明了问题式（0.1）中存在无限多具有任意大能量的非径向正解。我们相信，我们在本文中使用的各种新思路和计算技术将有助于处理其他涉及卷积非线性项的相关椭圆问题。

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.