报告人：罗鹏（华中师范大学）

报告题目：The positive ground state solution on nonlinear Schrodinger equations

报告摘要：We are concerned with the following nonlinear Schr\"odinger equation

\begin{equation*}

-\varepsilon^2\Delta u+ V(x)u=|u|^{p-2}u,~u\in H^1(\mathbb{R}^N),

\end{equation*}

where $\varepsilon>0$ is a small parameter, $N\geq 1$, $2<p<2^*$.

For a class of $V(x)$ which attains the minimum at a closed hypersurface $\Gamma$, we give the location of the concentrated point to the positive ground state solution and establish the local uniqueness of the positive solution with concentration under certain conditions on $V(x)$, which implies the uniqueness of positive ground state solution. Also some partial symmetry can be obtained by the uniqueness. Here our main tools are the local Pohozaev identities and blow-up analysis. And the crucial key is to analysis the precise algebra relation of the concentrated point caused by the degeneracy and inhomogeneity of $V(x)$ at this point.

报告人简介：罗鹏，华中师范大学数学与统计学学院副教授。2014年6月博士毕业于武汉大学数学与统计学院，2016年6月博士后出站于中国科学院数学与系统科学研究院。研究方向为偏微分方程及其应用，主要研究兴趣是椭圆方程解的集中现象。主持中国博士后科学基金和国家自然科学基金青年项目等。主要成果发表在JMPA，CVPDE，JDE等SCI期刊。

报告时间：2018年6月14日（星期四）11：00-12：00

报告地点:科技楼南702