A magnetic Schr\"{o}dinger equation with exponential critical growth in $\mathbb{R}^{2}$

2020年10月23日13:00-14:00  闵行数学楼102报告厅

*主持人：叶东 教授
*时间：2020年10月23日13:00-14:00
*地点：数学楼102 报告厅

*讲座内容简介：
In this thalk, we are concerned with the following nonlinear Schr\"{o}dinger equation with magnetic field
\begin{align*}
\Big(\frac{\varepsilon}{i}\nabla-A(x)\Big)^{2}u+V(x)u=f(|u|^{2})u,\quad x\in\mathbb{R}^{2},
\end{align*}
where $\varepsilon>0$ is a parameter, $V:\mathbb{R}^{2}\rightarrow \mathbb{R}$ and $A: \mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ are continuous
potentials and $f:\mathbb{R}\rightarrow \mathbb{R}$ has exponential critical growth. Under a local assumption on the potential $V$, by variational methods, penalization technique, and Ljusternick-Schnirelmann theory, we show multiplicity and concentration of solutions for $\varepsilon$ small. This is a joint work with professor Pietro d'Avenia.

*主讲人简介：