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

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

引用次数: 3

Abstract

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

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。

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

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