应304am永利集团官网杨四辈教授和耿俊教授邀请，华南师范大学钟学秀副研究员将于2023年10月17日进行线上学术报告，欢迎全校师生参加.

报告题目：Normalized solutions for nonlinear Schr\"odinger equations with general nonlinearities and Sobolev critical exponents

时  间：2023年10月17日（星期二）下午14:30;

地  点：腾讯会议（会议ID：375-483-950）

报告摘要：We study the existence, multiplicity of prescribed mass positive solutions to a Schr\"odinger equation of the form

$$-\Delta u-\lambda u=f(u), u\in H^1(\R^N), N\geq 3,$$

where $f\in C(\R,\R)$ is a very general nonlinearity having a Sobolev critical growth. We mainly study the pure mass supercritical case and the mass mixed critical case. Precisely, for the pure mass supercritical case, under related mild assumptions, we establish the existence of mountain pass normalized solution for all prescribed mass $c>0$. We also capture its precise asymptotic behavior as $c\rightarrow 0^+$ as well as $c\rightarrow +\infty$. For the mass mixed case, we can find at least two different positive normalized solutions for small $c>0$. One is a local minimizer and the other one is a mountain pass solution. We also establish a sequence of properties for the local minimizer including the uniqueness, asymptotic behavior,etc. The asymptotic behavior of the mountain pass solution as $c\rightarrow 0^+$ is also studied. This is a joint work with Prof. Vicentiu D. Radulescu, Prof. Jianjun Zhang and Dr. Jinfang Zhou.

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报告人简介

钟学秀，华南师范大学副研究员，华南数学应用与交叉研究中心青年拔尖引进人才。研究方向为运用非线性分析、变分法等方法来研究几何分析学、数学物理中椭圆型偏微分方程和方程组以及某些不等式问题。主持国家青年基金和面上基金各一项。已在J.Differential Geom.，Math. Ann.，Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)，Calc. Var. PDE，J. Differential Equations等国际重要刊物上发表多篇学术论文。在非线性泛函分析和椭圆偏微分方程领域的Li-Lin公开问题，Sirakov公开问题，Bartsch-Jeanjean-Soave公开问题，Bartsch-Li-Zou公开问题等方面获得了重要进展。

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