應(yīng)yl7703永利官網(wǎng)楊四輩教授和耿俊教授邀請，華南師范大學(xué)鐘學(xué)秀副研究員將于2023年10月17日進(jìn)行線上學(xué)術(shù)報(bào)告，歡迎全校師生參加.

報(bào)告題目：Normalized solutions for nonlinear Schr\"odinger equations with general nonlinearities and Sobolev critical exponents

時(shí)  間：2023年10月17日（星期二）下午14:30;

地  點(diǎn)：騰訊會議（會議ID：375-483-950）

報(bào)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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報(bào)告人簡介

鐘學(xué)秀，華南師范大學(xué)副研究員，華南數(shù)學(xué)應(yīng)用與交叉研究中心青年拔尖引進(jìn)人才。研究方向?yàn)檫\(yùn)用非線性分析、變分法等方法來研究幾何分析學(xué)、數(shù)學(xué)物理中橢圓型偏微分方程和方程組以及某些不等式問題。主持國家青年基金和面上基金各一項(xiàng)。已在J.Differential Geom.，Math. Ann.，Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)，Calc. Var. PDE，J. Differential Equations等國際重要刊物上發(fā)表多篇學(xué)術(shù)論文。在非線性泛函分析和橢圓偏微分方程領(lǐng)域的Li-Lin公開問題，Sirakov公開問題，Bartsch-Jeanjean-Soave公開問題，Bartsch-Li-Zou公開問題等方面獲得了重要進(jìn)展。

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萃英學(xué)院

2023年10月16日