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 1.8 4区数学 Q1 MATHEMATICS

Differential and Integral Equations 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

Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.