具有指数临界非线性的平面Schrödinger-Poisson系统归一化解的存在性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-28 DOI:10.57262/die036-1112-947

C. O. Alves, E. D. S. Boer, O. Miyagaki

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引用次数: 3

摘要

在本工作中，我们关注以下Schr“odinger-Poisson系统$$\left\｛\bbegin｛array｝｛ll｝-\Delta u+\lambda u+\mu（\ln|\cdot|\ast|u|^｛2｝）u=f（u）\textrm｛\In\｝\mathbb｛R｝^2，\\intR|u（x）|^2 dx=c，\c>0，\end｛array｝\right。$$对于$\mu\in\R$和具有指数临界增长的非线性$f$。这里$\lambda\in\R$代表拉格朗日乘数，它是未知的一部分。我们的主要结果扩展和/或补充了在\cite{Ji}和\cite{[cjjj]}中发现的一些结果。

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Existence of normalized solutions for the planar Schrödinger-Poisson system with exponential critical nonlinearity

In the present work we are concerned with the existence of normalized solutions to the following Schr\"odinger-Poisson System $$ \left\{ \begin{array}{ll} -\Delta u + \lambda u + \mu (\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ \ in \ } \mathbb{R}^2 , \\ \intR |u(x)|^2 dx = c,\ c>0 , \end{array} \right. $$ for $\mu \in \R $ and a nonlinearity $f$ with exponential critical growth. Here $ \lambda\in \R$ stands as a Lagrange multiplier and it is part of the unknown. Our main results extend and/or complement some results found in \cite{Ji} and \cite{[cjj]}.

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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.