报告题目：Normalized solutions for logarithmic Schr\{o}dinger equation with a perturbation of power law nonlinearity

报告人：帅伟副教授，华中师范大学

报告时间：2023年04月20日16：00-17：00

报告方式：腾讯会议，会议号：940-338-079

报告摘要：We discuss the existence of normalized solutions to the following logarithmic Schr\{o}dinger equation

\begin{equation*}\label{eqs01}-\Delta u+\lambda u=\alpha u\log u^2+\mu|u|^{p-2}u, x\in\R^N, \end{equation*} under the mass constraint \[\int_{\R^N}u^2\mathrm{d}x=c^2,\] where $\alpha,\mu\in \R$, $N\ge 2$, $p>2$, $c>0$ is a constant, and $\lambda\!\in\!\R$ appears as Lagrange multiplier. Under different assumptions on $\alpha,\mu,p$ and $c$, we prove the existence of ground state solution and excited state solution. The asymptotic behavior of the ground state solution as $\mu\to 0$ is also investigated. Our results including the case $\alpha<0$ or $\mu<0$, which is less studied in the literature. This is a joint work with Dr. Yang Xiaolong.

报告人简介： 帅伟，华中师范大学副教授，博士生导师。主要研究方向是非线性椭圆型偏微分方程、非线性泛函分析，主持完成国家基金青年项目1项，现主持国家自然科学基金面上项目1项。主要成果发表在Journal of Function Analysis、Calculus of Variations and Partial Differential Equations、Nonlinearity、Journal of Differential Equations等国际期刊上。

邀请人：非线性分析与PDE团队