Multiplicity and concentration results for a magnetic Schrodinger equation with exponential critical growth in \mathbb{R}^{2}

报告题目：Multiplicity and concentration results for a magnetic Schrodinger equation with exponential critical growth in \mathbb{R}^{2}

报告人：姬超副教授

报告时间：2022/6/3 15:00-16:00

报告形式：腾讯会议

会议ID：495-822-611

会议密码：123456

报告摘要：In this talk, we are concerned with the  following nonlinear magnetic Schr\{o}dinger equation

\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 and a global assumption on the potential $V$ respectively, we show multiplicity and concentration of solutions for $\varepsilon$ small. This is a joint work with Professor Pietro d'Avenia.

报告人简介：姬超，华东理工大学副教授，2009年于兰州大学获得博士学位，师从范先令教授。他的研究方向是非线性偏微分方程，变分和拓扑方法，在包括 Science China Mathematics, IMRN, IJM, CVPDE, JLMS, JDE, JGA, DCDS等国际知名刊物上发表SCI论文50篇。现主持国家自然科学基金面上项目和上海市自然科学基金各一项，现为《Mathematical Methods in the Applied Sciences》和《Discrete & Continuous Dynamical System-S》等多个国际刊物编委。