應(yīng)yl7703永利官網(wǎng)楊璐教授和耿俊教授的邀請(qǐng)，江西師范大學(xué)yl7703永利官網(wǎng)龍薇教授將于2021年7月16日—7月20日訪問我校。屆時(shí)將舉辦專題學(xué)術(shù)講座，熱忱歡迎各位老師、研究生的參加.

報(bào)告題目：Henon equation in a general domain by Pohozaev identities and Reduction Method

時(shí)    間：2021年7月20日(星期二)上午10:00;

地    點(diǎn)：理工樓518.

報(bào)告摘要：

In this talk, we are concerned with the following H\'{e}non problem \begin{equation*}\label{eq1} \left\{\begin{array}{ll} \Delta u= |x|^\alpha u^{2^*-1-\varepsilon} ,\ \ u>0,\ \hspace{3mm} & \text{ in } \ \ \Omega,\\

u=0,\ \ \hspace{3mm}&\text{ on } \ \ \partial\Omega，\end{array} \right.

\end{equation*} where $N\geq 4$, $2^*=\frac{2N}{N-2}$, $\alpha >0$, $\ep$ is a small positive parameter, $\Omega $ is a smooth bounded domain in $\r^N$ and $0 \in \Omega$. Most of previous works for H\'{e}non problems were investigated in special domains, such as balls and annulus. In this paper, we will study the case when $\Omega$ is a more general domain, which does not satisfy symmetry any more. We first investigate the necessary condition on the location of the blow up point for the peak solution to the above H\'{e}non problem. Then, we prove that, as $\varepsilon\rightarrow 0$, the above problem has a positive solution with multiple bubbles under a suitable condition on the geometry of $\Omega$.

歡迎廣大師生參加！

龍薇教授簡(jiǎn)介

龍薇，女，教授、博士生導(dǎo)師、江西省“杰青”，主要從事偏微分方程與非線性分析的研究。近年來，在Ann. Sc. Norm. Super. Pisa Cl. Sci.、J. Differential Equations、Proc. Roy. Soc. Edinburgh Sect. A等國(guó)際權(quán)威期刊發(fā)表學(xué)術(shù)論文30多篇；承擔(dān)了7項(xiàng)國(guó)家自然科學(xué)基金的研究（主持面上和青年項(xiàng)目各1項(xiàng)）；獲省自然科學(xué)獎(jiǎng)二等獎(jiǎng)、省高?？萍汲晒?jiǎng)一等獎(jiǎng)各1次；擔(dān)任了美國(guó)數(shù)學(xué)評(píng)論和德國(guó)數(shù)學(xué)文摘評(píng)論員；指導(dǎo)的學(xué)生多人獲國(guó)家獎(jiǎng)學(xué)金、省政府獎(jiǎng)學(xué)金、省優(yōu)秀碩士學(xué)位論文、數(shù)學(xué)建模競(jìng)賽獎(jiǎng)等榮譽(yù)。

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2021年7月16日